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ABSOLUTE  ATOMIC  WEIGHTS 


CHEMICAL   ELEMENTS 


CHEMISTS  OF  THE  NINETEENTH  CENTURY 


UNITY  OF   MATTER; 

GENERAL  SCIENTIFIC  PUBLIC, 


GUSTAVUS  DETLEF  HINRICHS,  M.D.,  LL.D,, 


PORTRAIT  OF  BERZELIUS  AND  THREE  PLATES. 


CARL  GUSTAV  HINRTC1! 


BERZELIUS. 


pp.  84-5. 


THE 

ABSOLUTE  ATOMIC  WEIGHTS 

OF    THE 

CHEMICAL  ELEMENTS 


ESTABLISHED  UPON  THE   ANALYSES 
....  OF  THE  .... 


CHEMISTS  OF  THE  NINETEENTH  CENTURY 


AND   DEMONSTRATING  THE 


UNITY  OF  MATTER; 


PRESENTED   IN   SIMPLE   LANGUAGE 
.  .  TO  THE  .  . 


GENERAL  SCIENTIFIC  PUBLIC, 


GUSTAVUS  DETLEF  H1NRICHS,  M.D.,  LL.D., 

*N 

Honorary  and  Corresponding  Member  of  Scientific  Societies  in 

Austria,  England,  France,  Germany  and  the  United  States; 
Professor  of  Chemistry  in  the  St.  Louis  College  of  Pharmacy. 


WITH  A  PORTRAIT  OF  BERZELIUS  AND  THREE  PLATES.  ^-      _  R       ^^ 

OF  THE     Y 

%  UNIVERSITY 

ST.  Louis,  Mo.,  U.  S. 

CARL  GUSTAV  HINRICHS,  PUBLISHER. 
1901. 


ALL   RIGHTS   RESERVED   BY  THE   AUTHOR. 

GENERAL 


Copyright,  1901. 
By  GUSTAVUS  DETLEF  HINRICHS. 


Printed  by  R.  P.  Studley  &  Co.,  St.  Louis,  Mo. 


I  do  not  accept  human  or  official 
authority,  but  exclusively  depend 
on  Nature.  Page  229. 

PROLOGUE. 

The  Atomic  Weights  of  the  Chemical  Elements  are  the 
most  important  of  all  numerical  values  of  Nature,  both 
practically  and  theoretically. 

Practically,  these  values  are  used  daily  in  all  the  labora- 
tories throughout  the  world  for  the  reduction  of  analyses, 
and  in  the  chemical  manufactories  for  the  estimation  of  the 
proportions  of  materials  to  be  used  and  to  check  the  prod- 
uct obtained. 

If  the  atomic  weights  so  used  are  in  error,  even  the  best 
made  chemical  analyses  will  necessarily  be  falsified  by  such 
error. 

Theoretically,  these  atomic  weights  must  be  known  with 
accuracy  to  permit  the  solution  of  the  highest  philosophical 
question  of  chemistry,  namely,  that  of  the  UNITY  OF 
MATTER. 

Let  us  briefly  trace  the  work  done  in  this  field. 

A  century  has  passed  since  Dalton  introduced  the  idea  of 
atomic  weights  into  the  science  of  chemistry. 

During  the  first  half  of  that  century,  the  great  chemist 
of  the  North,  BERZELIUS,  made  numerous  excellent  deter- 
minations of  the  atomic  weights  of  all  elements  then  known. 

Berzelius  himself,  and  his  School  which  comprises  many 
distinguished  German  Chemists,  such  as  Rose,  Mitscherlich 
and  Wohler,  employed  exclusively  rigid  methods,  mainly 
dry  way  operations.  No  fancy  work  of  any  kind  was  toler- 
ated. No  pretenses  to  extreme  accuracy  were  made,  and 
the  accuracy  of  the  balance  was  never  substituted  for  the 
skill  of  the  chemists.  No  gnats  were  strained  at  while 
swallowing  camels. 

About  1860,  STAS  of  Brussels,  started  in  an  opposite 
direction.  The  wet  way  silver  chloride  titration  was  made 
a  fundamental  operation.  Nitrates  and  chlorides  were  inter- 
changed. Large  quantities  of  matter  were  operated  upon. 
All  weights  were  ostentatiously  reduced  to  vacuum. 


105)031 


PROLOGUE. 


The  use  of  large  quantities  and  the  extreme  accuracy 
apparently  attained  had  the  effect  intended.  The  leading 
official  chemists,  and  through  them,  the  academies  and 
chemical  societies,  instantly  accepted  the  published  results 
and  overwhelmed  Stas  with  honors. 

As  a  matter  of  course,  the  final  conclusion  of  STAS  was 
also  accepted:  the  atomic  weights  of  the  chemical  elements 
have  no  common  divisor,  and  therefore,  the  chemical  ele- 
ments cannot  have  their  origin  in  one  primitive  substance. 

The  expression  of  any  doubt  in  either  the  accuracy  of 
Stas'  atomic  weights  or  the  truth  of  his  philosophic  con- 
clusion, has  for  almost  forty  years  been  considered  an 
evidence  of  lack  of  scientific  intelligence.  The  Unity  of 
Matter  was  pronounced  a  chimera. 

The  position  of  Stas  and  his  school  was  very  much 
strengthened  by  the  elaborate,  though  very  faulty,  recalcu- 
lations of  his  analyses  by  prominent  chemists,  such  as 
Lothar  Meyer  and  Ostwald  in  Germany,  Julius  Thomsen 
and  Sebelien  in  Denmark,  Van  der  Plaats  in  Holland,  and 
Frank  Wigglesworth  Clarke  in  the  United  States. 

The  work  of  Clarke  is  properly  considered  representing 
even  the  Government  of  the  United  States.  For  Clarke  is 
Chief  Chemist  of  the  Geological  Survey,  under  the  Secretary 
of  the  Interior;  his  recalculations  have  been  formally 
endorsed  by  the  Secretary  of  the  Smithsonian  Institution 
and  published  officially  at  the  expense  of  the  Smithson 
Fund;  it  has,  finally,  been  sent  out  under  the  official  frank 
as  registered  matter.  The  deficiency  of  the  postal  service — 
partly  so  resulting — is  made  up  by  Congressional  appropria- 
tions. 

The  same  author  Clarke  is  also  habitually  sent  by 
authority  of  the  National  Government  and  at  public  expense, 
as  delegate  to  Congresses  of  Chemists,  and  put  in  charge  of 
National  Exhibits  at  home  and  abroad.  This  highest  pos- 
sible official  consideration  has  enabled  him  to  exercise  a 
ruling  influence  in  the  American  Chemical  Society. 

A  critical  examination  of  the  work  of  Stas,  and  especially 
of  the  recalculations  of  Clarke,  is  therefore  not  only  a  diffi- 
cult, but  also  an  extremely  hazardous  undertaking;  only  the 


PROLOGUE. 


absolute  conviction  of  duty  to  truth  and  science  induced 
and  sustained  me  in  this  work. 

I  found  even  enormous  errors  of  reduction  to  vacuum 
committed  by  Stas,  but  overlooked  by  all  his  recalculators. 
I  discovered  systematic  errors  in  his  syntheses  of  silver 
and  lead  nitrate,  which  make  it  impossible  to  use  these 
vaunted  syntheses  for  any  atomic  weight  determination 
whatever.  The  silver  chloride  process  is  unfit  for  such  use 
because  it  takes  a  sort  of  body-guard  of  salt  to  keep  the 
silver  chloride  down  as  a  precipitate. 

These  results  of  mine  were  published  in  the  Comptes 
Rendus  of  the  Academy  of  Sciences  of  Paris,  from  1892 
to  1894,  and  more  fully  in  my  TRUE  ATOMIC  WEIGHTS 
of  1894. 

Some  of  the  most  eminent  Chemists  and  Physicists  have 
admitted  these  critical  results,  which  have  also  been  taught 
in  one  of  the  most  famous  Universities  of  the  world,  and 
have  been  published  with  approval  in  chemical  periodicals 
and  special  treatises. 

In  1897,  the  Smithsonian  Institution  issued  a  second 
edition  of  Clarke's  Recalculations,  in  which  my  work  is 
grossly  misrepresented.  These  false  atomic  weights  of 
Clarke  and  the  Smithsonian  Institution  have  recently  been 
forced  upon  the  attention  of  the  Committee  of  Revision 
of  the  United  States  Pharmacopoeia  for  adoption. 

I  have,  therefore,  deemed  it  advisable  to  present  my 
work  in  the  simplest  possible,  most  elementary  form,  so 
that  every  one  interested  in  the  great  scientific  and  public 
questions  involved  may  understand  the  issue. 

Since  the  false  science  is  backed  by  Government 
Authority  and  published  by  the  means  of  the  Smithsonian 
Institution,  and  sent  free  through  the  registered  mail  by 
official  frank,  I  have  endeavored  to  put  this  work  at  an 
almost  nominal  price  within  the  reach  of  all. 

This  work  is  herewith  most  respectfully  submitted  to 
the  General  Scientific  Public,  which  I  believe  is  vitally 
interested  in  this  scientific  question  itself,  and  in  the 
questions  of  scientific  morals  and  administration  involved. 

The   question   of  science   is   one   of  the    greatest    ever 


VI  PROLOGUE. 


raised,  namely:    Is  the  material  universe  composed  of  one 
single  substance  or  of  many  chemical  elements? 

Our  work  shows  that  the  unity  of  matter  is  established 
with  greater  certainty  than  any  other  principle  of  scientific 
philosophy. 

By  our  true  and  absolute  atomic  weights,  the  almost 
universal  practice  of  falsifying  the  results  of  chemical 
analyses  by  reducing  them  with  false  atomic  weights,  will 
be  stopped. 

All  chemical  analyses  made  for  many  years  in  our 
Government  laboratories  have  been  so  falsified  by  the 
use  of  the  false  Smithsonian  Atomic  Weights  of  Clarke. 
The  question  of  scientific  morals  is  this :  Are  official 
leaders  in  science,  at  home  and  abroad,  presenting  to  and 
endorsing  before  the  world,  scientific  data  and  doctrines, 
which  by  a  little  careful  examination,  they  ought  to  recog- 
nize themselves  as  totally  false  and  contradicted  by  experi- 
ment and  observation,  and  which  have  been  demonstrated 
false  in  my  publications  specified? 

The  question  of  scientific  administration  is  naturally 
primarily  addressed  to  the  citizens  of  the  United  States, 
as  follows: 

(<  THE  SMITHSONIAN  INSTITUTION, 

founded  for   the  Increase  and   Diffusion  of   Knowl- 
edge among  men  per  orbem,"  and 
governed  by  a  Board  of  Directors,  appointed  by  the 

CONGRESS  OF  THE  UNITED  STATES, 
which  has  accepted  the  Trust  Fund  of  the  English- 
man Smithson  for  such  an  Institution; 

is  it  right  and  proper 

for  the   Secretary   of    that   Institution   to   issue   and 

indorse  a  work  which  can  only  Increase  and  Diffuse 

ERROR  and  FALSE  SCIENCE  among  men  per  orbem? 

The  proofs,  that  the  work  of  Clarke  specified  is  of  such 

a  kind  are  here  most  respectfully  submitted   in  this  book. 

In   these  United   States  we   never  had  a  State  Church, 

and  we  trust  we  shall  never  have  that  which  has  been  one 

of  the  greatest  curses  to  Europe ;  only  by  fearful  sacrifices 

— of  which  the  thirty  years'  war  was  merely   an  episode — 

Europe  has  partly  relieved  itself  thereof. 

But  will  a  STATE  SCIENCE  be  less  harmful  than  a  STATE 
CHURCH  ? 


PROLOGUE. 


Have  we  not  now  in  this  country,  quite  a  strong  State 
Science  supported  by  millions  of  dollars  of  public  funds 
annually,  and  rapidly  branching  into  all  spheres  of  activity? 

We  universally  blame  the  Inquisition  to-day  for  having 
condemned  Galileo  in  a  darker  age,  and  for  having  insisted 
upon  the  stability  of  the  earth  and  the  reality  of  the  motion 
of  the  sun  and  stars  around  our  earth.  Yet  this  Inquisition 
acted  in  the  performance  of  its  duty,  and  shielded  millions 
against  a  spiritual  danger  which  they  believed  to  be  very 
real  and  very  great.  v 

Besides,  the  Inquisition  had  the  testimony  of  the  actual   j  '  v" 
phenomena  in  their  favor,  for  the  visible   motions  of  the  I      /^  £    * 
heavens  exactly  conform  to  their  verdict.  / 

But  the  scientific  Secretary  of  the  Smithsonian  Institu- 
tion at  Washington,  in  1897,  delares  de  facto,  by  indorsing 
and  publishing  the  work  of  Clarke,  that  chemical  action 
changes  the  weight  of  matter,  which  is  not  only  contrary 
to  all  experimental  evidence,  but  also  contrary  to  a  univers- 
ally accepted  axiom  of  philosophy  and  science. 

The  Secretary  of  the  Smithsonian  Institution  declaring 
officially  to  be  true  that  which  was  demonstrated  false,  and 
using  the  funds  of  that  Institution  and  its  franking  privi- 
lege to  distribute  these  gross  errors  and  falsehoods  among 
men  per  orbem — was  not  (as  were  the  members  of  the 
Inquisition)  acting  in  the  performance  of  his  duty,  which 
demands  that  the  Smithson  Fund,  in  trust  given  our 
National  Congress,  shall  be  used  for 

"  the  Increase  and  Diffusion  of  KNOWLEDGE  among 
({  men  per  orbem." 

The  absolute  atomic  weights  presented  in  this  our  work, 
are  true  to  nature,  for  they  are  based  upon  the  analyses  and 
determinations  of  the  most  reliable  chemists  and  physicists 
of  the  Nineteenth  Century,  from  Berzelius  to  Lord  Ray- 
leigh. 

I  most  respectfully  submit  the  evidence  collected  in  this 
book  to  the  General  Scientific  Public  and  to  the  Students 
of  Chemistry  throughout  the  World. 

GUSTAVUS  DETLEF  HINRICHS, 

4106  Shenandoah  Avenue, 
September,  1901.  ST.  Louis,  Mo.,  U.  S.  A. 


THE  TWELVE  MASTERS 
WHOSE   EXPERIMENTAL  DETERMINATIONS  CONSTITUTE 

THE  FOUNDATION  OF  OUR 

ABSOLUTE  ATOMIC  WEIGHTS 

IN  PARTS  SECOND  AND  THIRD. 

It  is  the  experimental  work  of  these  Masters  we  make  use 
of — their  personal  opinion  (generally  opposite  of  our  own), 
or  even  their  calculated  final  values  of  atomic  weights 
(generally  obtained  by  erroneous  methods)  are  of  no  special 
interest  in  this  study.  The  order  is  that  of  the  principal 
publication. 

BERZELIUS,  JONS  JACOB.  Born  August  27,  1779,  at  West- 
erlosa,  Oestergotland ;  died  August  7,  1848,  at  Stockholm, 
SWEDEN.  "  The  Greatest  Chemist  of  the  World,"  see  pp. 
84-85.  Portrait,  see  Frontispiece,  representing  him  in 
early  life. 

1810-1830,  LEAD,  74-91,  263.  Also:  Al,  226.  As,  231. 
Ba,  235.  Bo,  238.  C,  101.  Fe,  91-94.  Fl,  242. 
Pd,  263.  Pt,  116.  Sn,  267.  Te,  269-270.  Rule,  3. 
Balance,  41-43.  Methods,  49.  Gnat  and  Camel,  83. 
Mention  throughout  this  book. 

TURNER,  EDWARD.  Born  in  Jamaica,  1798;  died  Feb- 
ruary 13,  1837,  in  London,  ENGLAND.  The  first  Professor 
of  Chemistry,  University  College. 

1833,    CHLORINE,    97-99,    240.       Also:    Pb,    87,    89. 

Ba,  235-236. 

DUMAS,  JEAN-BAPTISTE.  Born  July  15,  1800,  at  Alais; 
died  April  n,  1884,  at  Cannes,  FRANCE.  For  years  the 
leading  Chemist  of  France,  occupying  the  highest  scientific 
and  Government  positions  at  Paris. 

1840,     CARBON  -  DIAMOND,    39,     101-105,     238,     262. 


Graphite,   48,  ^03.     Alsoj    Al,   226.     Ba,   236-237. 
~1,  243.     Mo,  260.     P,  263. 
Pb,   89.     S,   264.  "  Sb,   266.     Si,  267.     Sn,  267-268. 


Ca,  106-107.     Cd,  240.     Fl,  243.     Mo,  260 
Pb,   89.     S,   264.     Sb, 
Sr,  268.     Wo,  274-275. 

Balance,    40.       Titrations,    55.       Skill,    iio-m. 
Mention,  138,  157,  211,  etc. 

ERDMANN,  OTTO  LINNE.  Born  April  n,  1804,  at  Dres- 
den ;  died  October  9,  1869,  at  Leipzig,  GERMANY.  Professor 
of  Chemistry,  University  of  Leipzig. 

1844,  MERCURY,  49,  61-63,  95-97,  257.  Also:  C,  102- 
104.  Ca,  50,  106-107.  Cu,  242.  Fe,  93-94.  Se,  267. 
Mention,  112,  138,  167,  etc. 


THE    TWELVE.  IX 


MARCHAND,  RICHARD  FELIX.  Born  August  25,  1813,  at 
Berlin ;  died  August  2,  1849,  at  Halle,  GERMANY.  Professor 
of  Chemistry,  University  of  Halle. 

1844,  SULPHUR,  96-97.   Also:  Mg,  108.  Wo,  273.   With 

Erdmann:     C,  Ca,  Cu,  Se.     Mention,  167,  211,  etc. 

SVANBERG,  LARS  FREDERIK.     Born    May  5,  1805;    died 

July  16,  1878,  at  Upsala,  SWEDEN.     Professor  of  Chemistry, 

University  of  Upsala. 

1844,  IRON,  91-95,  242.     Also:  Hg,  98.     Mention,  112, 

138,  211,  etc. 

SCHEERER,    KARL    JOHANN    AUGUST    THEODOR.     Born 

August  28,  1813;  died  July  19,  1875,  at  Dresden,  GERMANY. 

1850,   MAGNESIUM,   50,    108-109,   114,  260.     Mention, 

138,  211. 

CROOKES,  SIR  WILLIAM.    Born  June  17,  1832,  at  London, 
ENGLAND.     Founder  of  the   Chemical   News.     Researches 
on  Radiation  in  High  Vacua.     Discovered  Thallium,  1861. 
1873,  THALLIUM,  120-138,  271,  281-4.     Also:    89,  139- 

140,  169,  181,  209,  214,  218,  281,  294. 

SEUBERT,  KARL  FRIEDRICH  OTTO.  Born  April  6,  1851, 
at  Karlsruhe,  Baden.  Professor  of  Chemistry  at  Tubingen, 
now  at  Hanover,  GERMANY. 

1881,  PLATINUM,  115-119,  264.   Also:  Ir,  258.    Mo,  260. 
Os,  262.     Rh,  264.     Mention,  50,  75,  138,  211. 

RAMSAY,  WILLIAM.  Born  October  2,  1852,  at  Glasgow, 
Scotland.  Professor  of  Chemistry,  University  of  London, 
and  University  College,  London,  ENGLAND.  Nullovalent 
Gases  in  the  Atmosphere. 

1893,  BORON,  141-151,  238.    Also:  33,  42,  43,  53,  63, 
123,  211,  217. 

ASTON,  Miss  EMILY,  B.  Sc.  (Univ.  of  London).  Associ- 
ated with  Professor  Ramsay  in  his  great  work  on  Boron, 
1893.  ENGLAND. 

1893,  SODIUM,  147-148,  261. 

RAYLEIGH,  LORD.  Born  November  12,  1842,  at  Lang- 
ford  Grove,  Essex,  ENGLAND.  Successor  to  Maxwell  at 
Cambridge,  1879.  Professor  of  Natural  Philosophy  at  the 
ROYAL  INSTITUTION  OF  GREAT  BRITAIN,  an  Institution  with- 
out a  peer  in  the  world  (maintained  by  a  Society,  and  entirely 
independent  of  the  Government).  Discoverer  of  Argon. 

1895,  NITROGEN,  159-165,  201,  260.     HYDROGEN,  244. 
Also:  Ur,  272-273. 


CONTENTS. 

Prologue,    ni-vii. 
PART  FIRST. 

THE  ERRORS  OF  PRECISION  IN  ATOMIC  WEIGHT 
DETERMINATIONS. 

I.  GENERAL  INTRODUCTION: 

The  Chemical  Problem,  i.  The  Mathematical  Prob- 
lem, 3.  The  Probable  Error,  4.  The  Constant  Error, 
5.  Two  Common  Errors,  5.  Our  Course  of  Train- 
ing, 6. 

II.  THE  MEAN  WEIGHT  OF  A  SILVER  DOLLAR: 

Procedure,  7.  Determinations,  7.  Mean  Weight 
not  True  Weight,  8.  Effect  of  Wear;  Abrasion,  8. 
Frequency  in  Circulation,  8.  The  Mean  a  Lower 
Limit,  9.  Amount  of  Abrasion,  9.  Calculated  Weight 
of  New  Coin,  10.  Testing  the  Result;  Tolerance,  10. 
Estimate  from  Quarters,  u. 

III.  THE  PROBABLE  ERROR  OF  THE  MEAN: 

The  Two  Probable  Errors,  n.  Systematic  and  Con- 
stant Errors,  12.  Calculation  of  Probable  Error,  12. 
Shall  we  use  this  Error,  14.  Condition  by  Number,  15. 
Condition  by  Probability,  15.  Conditions  were  Dis- 
regarded, 16.  Conditions  Applied  by  Us,  16.  All  Pub- 
lished Probable  Errors  are  False,  17.  The  Double 
Distilled  Fraud,  18.  The  Law  of  Probability,  18.  All 
Dice  are  Loaded,  18.  False  Science  from  False  Facts 
and  False  Tools,  19.  Nature  can  not  be  Suppressed,  19. 
The  Exact  Scientist  Should  be  Tested  First,  20.  The 
Greatest  False  Scientist,  20. 


CONTENTS.  XI 


IV.  THE  CONSTANT  ERROR  OF  THE  MEAN: 

Constant  Error  of  Coins,  20.  Lower  and  Higher 
Limit,  21.  Laboratory  Work  Alone  not  Enough,  21. 
Observatory  Work  Alone  not  Enough,  22.  What  Ails 
the  Mean,  22.  Constant  Errors  Large,  23. 

V.  ACTUAL  ERRORS  OF  THE  MEAN: 

Mallet's  Determinations  of  the  Atomic  Weight  of 
Gold,  24.  The  Seven  Means  are  all  Mean,  25.  Our 
Little  Diagram  Shows  the  Facts,  26.  Mallet  did  not 
Hit  the  Mark,  26.  If  we  don't  Know  the  Tenth,  we 
don't  Know  the  Thousandth,  27.  Mallet  Suffers  from 
Morbus  Stasii,  27.  Our  Conclusion,  28. 

VI.  ERRORS  IN  PRECISION: 

The  Common  Practice,  28.  The  Two  Fatal  Com- 
mon Errors,  29.  Don't  Give  us  Your  Fancy  for  Fact, 
29.  Edgar  F.  Smith  and  W.  L.  Hardin,  30-32. 

VII.  ERRORS  DUE  TO  FALSE  DATA: 

Adopting  Data,  32.  Ramsay  and  Aston,  33.  H. 
Moissan  and  H.  Gautier,  34.  Armand  Gautier  and  J. 
Aloy,  35.  My  Method  in  the  Comptes  Rendus,  37. 

VIII.  ERRORS  OF  WEIGHING  : 

Weighing  First  and  Last,  38.  Dumas'  Combustion 
of  the  Diamond,  39.  Precision  of  Weighing,  40.  The 
Balance  used  by  Dumas,  40.  The  Balance  used  by  Ber- 
zelius,  41.  Our  Fine  Balances,  41.  Weighing  the 
Weighers,  42.  Great  Chemist,  Poor  Balance,  43.  The 
Man  and  the  Balance,  44.  Official  Rule,  44.  True  and 
Sham  Accuracy,  45.  The  Number  of  Decimals,  45.  A 
Fine  Probable  Error,  46. 

IX.  MINUTE  CHEMICAL  ERRORS: 

Chemical  Processes,  46.  Our  Standard  of  Matter, 
48.  Oxidation  of  Metals,  49.  Dry  Way  Processes  and 
Crystals,  49-51. 

X.  LARGER  CHEMICAL  ERRORS: 

Purification  by  Distillation,  51.  Good  Special 
Methods,  52.  Methods  Giving  Varying  Results,  53. 
False  Methods,  54.  Louis  Henry  of  Louvain,  56-57. 


XII  CONTENTS. 


PART  SECOND. 

THE  ABSOLUTE  ATOMIC  WEIGHT  OF  TEN 
LEADING  ELEMENTS. 

I.  OUR  METHOD  OF  DETERMINATION: 

Errors  Indicated,  58.  Absolutely  Fixed  Points 
Needed,  58.  Standard  Atomic  Weights,  59.  Table  of 
Same,  59.  Method  of  Procedure,  60.  Example:  Mer- 
cury, 61.  Extremes  and  Range,  62.  Determination  by 
Sight,  63.  Order  of  Procedure,  63.  Atomic  Weight 
Calculation  made  Easy,  64.  (Addendum :  Reduction  to 
Air,  278).  Standard  and  True  Atomic  Weights,  65. 
Our  Earlier  Publications,  66.  Baculus  vs.  Bacillus,  67. 
THE  WEIGHT  OF  A  HALF-EAGLE  : 

The  Importance,  67.  The  Mean  Weight  of  the  Half- 
Eagle,  68.  Frequency  of  Circulation,  70.  Amount  of 
Abrasion,  70.  Criminal  Extrapolation,  71.  The  Ratio 
and  the  Excess,  73. 

II.  THE  ATOMIC  WEIGHT  OF  LEAD,  BERZELIUS: 

Introduction,  74.  A,  Lead  Carbonate  Ignited,  74. 
B,  Lead  Oxide,  Wet  Way,  76.  C,  Lead  Oxide,  Dry 
Way,  Earliest  Work,  77.  Clarke  Falsifying  the  Record 
of  Berzelius,  78.  D,  Lead  Oxide,  Dry  Way,  Later 
Work,  79.  Berzelius'  Reduction  of  Lead  Oxide,  Si. 
How  I  Learned  the  Name  Berzelius,  84.  F,  Other  Pro- 
cesses, 85.  What  Shall  be  Done  with  Faulty  Methods 
and  False  Results?  90-91. 

III.  THE  ATOMIC  WEIGHT  OF  IRON,  SVANBERG: 

Historic  Record,  91.  Results,  93.  Late  Work  by 
Richards,  94. 

IV.  THE  ATOMIC  WEIGHT  OF  MERCURY,  ERDMANN  : 

Results  and  Comments,  95-96. 

V.  THE  ATOMIC  WEIGHT  OF  SULPHUR,  MARCH  AND. 

Results  and  Comments,  96-97. 

VI.  THE  ATOMIC  WEIGHT  OF  CHLORINE,  TURNER: 

Results  and  Comments,  97.  Svanberg's  Distilla- 
tions, 98.  Good  Old  Chemists  Abused  by  Clarke,  99. 
Hardin's  Electrolyses,  100. 


CONTENTS.  XIII 


VII.  THE  ATOMIC  WEIGHT  OF  CARBON,  DUMAS. 

Results  and  Comments,  101.  A  False  Correction, 
102.  Combustion  of  Different  Sorts  of  Carbon,  104. 

VIII.  THE  ATOMIC  WEIGHT  OF  CALCIUM: 
Results  and  Comments,  106. 

IX.  THE  ATOMIC  WEIGHT  OF  MAGNESIUM,  SCHEERER: 

Results  and  Comments,  108.  Richards'  Determina- 
tions, no.  Richards  Excels  Dumas  4000  Times,  no. 
Richards  Really  Progressed  o.oi  only,  112.  Scheerer 
and  Richards,  114.  Tanagra  Atomic  Weights,  114. 
Postscript,  115. 

X.  THE  ATOMIC  WEIGHT  OF  PLATINUM,  SEUBERT  : 

Results  and  Comments,  115-119. 

XI.  THE  ATOMIC  WEIGHT  OF  THALLIUM,  CROOKES: 

Praemonitio,  120.  The  Atomic  Weight  of  Thallium, 
121.  Crookes' Determinations  of  Thallium,  122.  Test- 
ing the  Laboratory  Work  of  Crookes,  123.  Crookes 
Annihilates  Stas,  125.  Expurgation  of  Crookes'  Labor- 
atory Record,  127;  see  Addendum  II,  pp.  281-284.  The 
Royal  Society  must  Act,  131.  The  Foundation  of 
Modern  Science,  132.  The  Systematic  Error  of 
Crookes,  133.  Crookes'  Expurgated  Results,  134.  The 
Morbus  Stasii,  135.  Effect  of  Morbus  Stasii  on  Crookes' 
Work,  135.  Our  Final  Conclusion,  137. 

XII.  THE  BANEFUL  STASIAN  ERRORS: 

The  Case  Stated,  138.  The  Labyrinth  of  Stas,  138. 
Crookes  Falsified  his  Work  by  Stas  False  Values,  139. 

PART  THIRD. 

THE  ABSOLUTE  ATOMIC  WEIGHTS  OF  BORON 
AND  NITROGEN. 

A.     Experimental  Determinations. 

I.     THE  ATOMIC  WEIGHT  OF  BORON,  RAMSAY: 

The  Work  Done,  141.  The  Weighings,  143.  Cor- 
relation of  Ratios  and  Atomic  Weights,  144. 


XIV  CONTENTS. 


II.  THE  ATOMIC  WEIGHT  OF  SODIUM,  ASTON. 

The  Work  Done,  147.  Confirmation  of  Cl  =  35.5, 
148.  The  Silver  Chloride  Process  Tested,  149. 

Determinations  by  Henry  Gautier,  152.  My  Carbide 
Process,  153.  La  Pleiade  de  Chimistes  d' Alsace,  154. 
Monsieur  Henri  Moissan,  155.  Friedel  and  Schiitzen- 
berger,  156. 

On  the  True  Atomic  Weight  of  Boron,  Hinrichs,  158. 

III.  THE  ATOMIC  WEIGHT  OF  NITROGEN,  LORD  RAYLEIGH  : 

Statement,  159.  Density  Determinations  and  Atomic- 
Weights,  160.  Atomic  Weight  of  Nitrogen,  1882,  160. 
Lord  Rayleigh's  Discovery,  161.  Density  Recognized 
for  Atomic  Weight  Determination,  163.  Why  did  not 
Clarke  Drop  Stas  at  the  End?  164.  Density  Determin- 
ations by  Leduc,  166.  Leduc's  Atomic  Weights,  167. 

B.    The  Folly  and  Fraud  of  Stas  and  his  School. 

Determinations  by  Chemical  Means,  169. 

I.  THE  CHALLENGE  OF  STAS: 

The  Challenge,  170.  Syntheses  of  Silver  Nitrate  by 
Stas,  174.  Table  of  Results,  177.  Postscriptum,  181. 

II.  THE  ATOMIC  WEIGHT  OF   NITROGEN    BY  CHEMICAL 

MEANS: 

Taken  according  to  Stas  and  Clarke,  182.  a.  Syn- 
thesis of  Silver  Nitrate,  186.  b.  The  Silver  Nitrate 
and  Potassium  Chloride  Ratio,  191.  c.  The  Meanest 
u  Mean  "  and  its  Impossible  Probable  Error,  195. 

III.  CHEMICAL  ACTION   CHANGES   WEIGHT  OF  MATTER: 

The  Old  Axiom,  198.  Clarke's  Grand  Discovery, 
199.  The  Author's  Confession,  201.  Die  Erhaltung  des 
Stoffes,  Ostwald,  203.  The  Two  Penitent  Brothers, 
Ostwald  and  Hinrichs,  204.  Ragnarok,  204. 

IV.  HERESY  IN  THE  CHURCH  OF  STAS  : 

Clarke  ignores  Landolt,  205.  How  does  Ostwald  get 
Manuscripts,  206.  The  great  Result  of  Landolt,  207. 
Annihilated  by  Clarke,  207.  Si  Quaeris,  Circumspice, 
207.  The  Conflict  Landolt-Clarke,  both  Stasians,  208. 
Reductio  ad  Absurdum,  209. 


CONTENTS.  XV 


C.    Conclusion. 

We  Rest  our  Case  Here,  209.  The  Maxim  of  Chee, 
210.  Is  Our  Demonstration  General?  211.  The  Work 
of  Four  Generations  of  Chemists,  212.  The  Probability 
of  our  Conclusion,  212.  Why  we  did  not  "  Select " 
the  Elements,  214.  Find  a  Needle  in  that  Haystack,  215. 
The  Base  of  that  Haystack,  216.  Why  our  Demonstra- 
tion Applies  to  All  Elements,  217.  The  Atomic  Num- 
ber, 217.  The  Honorable  Secretary  of  Berlin,  218. 


PART  FOURTH. 

TABULAR  VIEW  OF  THE  ATOMIC  WEIGHT 
ANALYSES  OF  THE  NINETEENTH  CENTURY. 

Introduction  and  Explanations,  219.  SILVER,  MAU- 
MENE,  221.  ALUMINUM,  225.  ARSENIC,  EDGAR  F. 
SMITH,  226.  Hibbs'  Direct  Weighings,  227.  Lost  in  the 
Wilderness  of  Error,  228.  No  Reduction  to  Vacuuum, 
229.  Kessler,  frei  nach  Heine,  231.  GOLD,  232.  Clarke 
Condemns  his  Own  Work,  234.  BARIUM,  235.  BERYL- 
LIUM, 237.  BISMUTH,  SCHNEIDER,  237.  BORON,  RAMSAY, 
238.  BROMINE,  MARIGNAC,  238.  CARBON,  DUMAS,  239. 
CALCIUM,  239.  CADMIUM,  v.  HAUER,  239.  CERIUM, 
240.  CHLORINE,  TURNER,  240.  COBALT,  CHROMIUM, 
Cesium,  241.  COPPER,  242,  IRON,  SVANBERG,  242. 
FLUORINE,  LOUYET,  242. 

HYDROGEN,  243-257.  LORD  RAYLEIGH,  244.  MOR- 
LEY'S  :  Determinations,  244;  show  of  Precision,  245; 
Weighings  of  Oxygen,  246;  of  Hydrogen,  248;  Ratio 
O  :  16,  252;  O  :  H,  253;  Hopeful  Progress,  256. 

STATE  SCIENCE  AND  STATE  CHURCH,  257. 

MERCURY,  ERDMANN,  257.  IODINE,  MARIGNAC,  258. 
IRIDIUM,  258.  Potassium,  Lanthanium,  Lithium,  259. 
MAGNESIUM,  SCHEERER,  260.  Manganese,  Molyb- 
denum, 260.  NITROGEN,  LORD  RAYLEIGH,  260.  SO- 
DIUM, MRS.  ASTON,  261.  Nickel,  Oxygen,  Osmium, 
262.  PHOSPHORUS,  SCHROETTER,  262.  LEAD,  BER- 


XVI  CONTENTS. 


ZELIUS,  263.  PALLADIUM,  263.  PLATINUM,  SEUBERT, 
264.  Rubidium,  Rhodium,  Ruthenium,  264.  SULPHUR, 
MARCHAND,  264.  ANTIMONY,  SCHNEIDER,  265  Edgar 
F.  Smith,  266.  SELENIUM,  PETTERSSON,  267.  SILICON, 
THORPE,  267.  TIN,  267.  Strontium,  268.  TELLURIUM, 
269.  TITANIUM,  H.  ROSE,  270.  THALLIUM,  CROOKES, 
271.  URANIUM,  EBELMEN,  271.  VANADIUM,  ROSCOE, 
273.  WOLFRAM,  SCHNEIDER,  273.  ZINC,  AXEL  ERD- 
MANN,  276.  ZIRCONIUM,  278. 

ADDENDA  TO  PART  SECOND. 

I.     Reduction  to  Air  (ad.  pp.  64-65),  278-281. 
II.     How   Crookes   Manufactured   Decimals   (ad.   p.   129), 
281-284. 

CONCLUDING  REMARKS. 

I.     The  Degree  of  Certainty  Attained,  285. 
II.     That  Stellar  Haystack,  288. 

III.  Table  of  Atomic  Numbers,  290. 

IV.  Atom    Mechanics,    Published    and    Prospective,    291. 
Epilogue,  292. 

SUPPLEMENTS. 

The  Twelve  Masters,  vm,  ix. 
The  Fifteen  Chemists,  296-297. 
Honor  List  of  Chemists,  298-300. 
Index  of  Names,  301-303. 
The  Mechanism  of  the  Aurora,  304. 

ILLUSTRATIONS. 

PORTRAIT  OF  BERZELIUS,  Frontispiece. 

Plate      I.  Facing  p.  24. 

Plate    II.  Facing  p.  176. 

Plate  III.  Facing  p.  192. 

ERRATA. 

No  serious  errata,  requiring  special  mention,  are  believed 
to  be  present. 


OF  THE 

UNIVERSITY 


PART  FIRST. 

The  Errors  of  Precision  in  Atomic 
Weight  Determinations. 

I.     GENERAL  INTRODUCTION. 

By  the  new  term  of  Absolute  Atomic  ./eight  we  desig- 
nate the  exact  number  expressing  the  atomic  weight  of  any 
element,  that  of  carbon-diamond  being  taken  at  f-velve 
exactly. 

We  are  well  aware  that  it  is  commonly  considered  im- 
possible to  determine  this  exact  atomic  weight.  But  we 
believe  this  opinion  of  chemists  of  the  present  due  to  their 
habit  of  considering  the  determinations  of  atomic  weights 
a  purely  laboratory  operation  only. 

The  determination  of  the  atomic  weight  of  any  element 
involves,  however,  two  entirely  distinct  problems,  the  one 
chemical,  the  other  mathematical. 

The  Chemical  Problem. 

The  chemical  problem  consists  in  the  production  of  the 
material,  its  chemical  change  into  some  other  definite  form, 
and  the  accurate  determination  of  the  ratio  of  the  weight  of 
these  two  materials. 

Such  a  process  we  have  in  the  reduction  of  pure  lead  oxide 
to  metallic  lead  when  moderately  heated  in  a  current  of  dry 
hydrogen. 

This  is  one  of  the  fundamental  processes  devised  by 
Berzelius. 

In  the  chemical  symbols,  also  devised  by  him,  the  above 
oxide  is  represented  by  Pb  O. 


THE    ERRORS    OF    PRECISION. 


The  weighings  give  the  ratio  Pb  O  :  Pb  =  a,  from  which, 
for  O  =  16  assumed,  the  value  for  the  atomic  weight  is  easily 
calculated. 

The  material  used  should  be  absolutely  pure,  the  change 
absolutely  complete  and  without  loss,  and  all  weighings 
absolutely  exact. 

Strictly  speaking,  it  is  impossible  to  produce  any  material 
in  an  absolutely  pure  condition.  It  is  equally  impossible  to 
completely  convert  any  such  substance  into  some  other  form 
of  combination,  without  loss  of  any  particle  of  matter,  or 
without  the  accession  of  any  particle  of  some  other  com- 
position or  nature. 

Hence  the  chemical  work  required  in  atomic  weight 
determinations  can  only  be  done  approximately,  not  with 
absolute  accuracy. 

In  other  words,  the  chemical  or  laboratory  work  can  only 
give  us  the  atomic  weight  affected  with  a  certain  mhinte 
error,  which  this  chemical  work  in  any  given  single  case  is 
unable  to  determine. 

By  varying  the  chemical  process  involved  in  the  deter- 
mination, we  therefore  find  different  values  for  the  atomic 
weight  of  the  same  element,  because  the  minute  chemical 
errors  involved  are  necessarily  different  in  the  different 
processes. 

Every  page  of  this  book,  giving  the  record  of  all  the 
chemical  determinations  actually  made  during  a  century,  will 
show  these  differences,  which  often  are  quite  considerable 
in  amount.  We  shall  as  an  example  for  this  introductory 
exposition,  give  all  the  results  obtained  by  Mallet  for  the 
atomic  weight  of  gold. 

For  these  reasons,  and  also  simply  as  a  matter  of  fact  and 
record,  the  mere  laboratory  work  of  the  chemist  cannot  give 
us  the  true  or  absolute  value  of  the  atomic  weight  of  any 
element.  The  empirical  values  so  obtained  we  shall  subject 
to  a  thorough  but  a  very  simple  mathematical  examination 
to  deduce  from  these  conflicting  empirical  values  the  true 
atomic  weight,  freed  from  the  unavoidable  errors  of  the 
laboratory  work. 


GENERAL    INTRODUCTION. 


The  Mathematical  Problem. 

The,  theoretical  or  mathematical  problem  to  be  solved  in 
order  to  obtain  the  true  or  absolute  atomic  weight  from  the 
varied  values  furnished  by  the  chemical  laboratory  work, 
has  hitherto  received  only  a  formal  treatment  in  the  use  of 
the  mean  and  its  probable  error.  We  must  briefly  consider 
this  formal  study  before  we  can  give  the  outline  of  our  own 
general  solution  of  the  problem. 

The  Mean. 

Chemists  have,  thus  far,  supposed  that  the  mean  value  of 
the  individual  chemical  determinations  is  nearer  the  true 
value  sought  for  than  any  of  the  actual  determinations  made. 

This  mean  value  is  calculated  by  summing  up  all  indi- 
vidual values  found  and  dividing  this  sum  by  the  number  of 
determinations  made. 

But  what  evidence  do  we  possess  proving  that  the  average 
of  the  individual  measures  is  the  true  measure?  Absolutely 
none  at  all. 

On  the  contrary,  every  chemist  will  readily  admit  that 
some  chemical  operations  necessarily  give  values  always  too 
high,  while  others  give  them  always  too  low.  The  great 
master  Berzelius  has  already  recognized  this  fact,  and  made 
it  the  basis  of  his  most  admirable  rule  of  procedure.  True 
At.  Weights,  p.  16. 

"Try  to  find  that  method  of  analysis,  in  which  the 
"  accuracy  of  the  result  will  depend  to  the  least  extent  on 
"  the  skill  of  the  operating  chemist;  and  when  this  method 
"  has  been  selected,  then  consider  what  unavoidable  con- 
"  ditions  are  present  which  may  cause  errors  in  the  result, 
ff  and  ascertain  whether  they  will  increase  or  diminish  the 
"  same.  Thereafter  make  another  determination,  in  which 
11  exactly  the  opposite  effects  only  can  be  produced.  If  the 
"  result  remains  the  same,  the  determination  was  correct." 
Sebelien,  p.  13,  quoted  from  Gilbert's  Annalen,  vol.  18,  p. 
537;  1814. 

This  rule  of  Berzelius  points  to  our  higher  and  lower 
limits,  between  which  the  time  atomic  weight  must  fall. 


THE    ERRORS    OF    PRECISION. 


We  must  most  positively  protest  against  the  universal 
assumption  that  the  mere  arithmetical  mean  of  the  experi- 
mental chemical  determination  is  the  true  value  of  the 
atomic  weight  of  any  element. 

But  since  this  declaration  is  in  conflict  with  universal 
practice,  it  may  be  advisable  to  first  present  a  simple  case 
from  common  experience  in  which  the  fallacy  of  the  mean 
is  palpable,  and  about  which  there  cannot  be  any  doubt. 

As  such  we  shall  give  the  case  of  the  determination  of  the 
weight  of  a  coin  of  given  value — a  common  silver  dollar — 
by  actually  weighing  a  number  of  such  coins  in  circulation. 

Having  done  this  work,  we  shall  be  able  to  understand 
why  the  mean  cannot  be  taken  as  the  true  value  in  most  cases. 

We  shall  thereby  be  relieved  from  one  of  the  most  com- 
mon errors  of  modern  scientific  practice. 

It  is  impossible  to  overlook  the  glaring  error  of  the  mean, 
since  according  to  the  object  or  cases  operated  upon,  the 
resulting  mean  values  do  differ  from  one  another,  as  a  matter 
of  fact.  See  the  atomic  weights  of  gold  determined  by 
Mallet,  pp.  24-28. 

The  Probable  Error. 

In  order  to  obtain  a  sort  of  indication  of  the  reliability 
of  such  a  mean,  chemists  have  tried  to  determine  the  "prob- 
able error"1"1  of  such  means  by  an  application  of  general 
principles  of  probability  put  into  practical  form  by  mathe- 
maticians. 

We  shall  therefore,  be  compelled  to  show  how  this  simple 
though  somewhat  tedious  calculation  is  effected,  and  above 
all,  call  attention  to  the  necessary  limitations  imposed  by 
mathematical  science,  under  which  alone  this  method  can 
possibly  be  used. 

We  shall  see  that  these  necessary  limitations  have  been 
overlooked  practically  in  all  the  applications  of  the  calcu- 
lation of  the  probable  error  made  by  chemists,  both  in 
America  and  in  Europe. 

To  what  an  extent  this  reckless  use  of  a  method  under 
conditions  where  it  is  absolutely  inapplicable  has  been 


GENERAL    INTRODUCTION*. 


carried,  will  be  shown  when  we  come  to  examine  the  Con- 
stants of  Nature  published  by  the  Smithsonian  Institution. 

We  shall  incidentally  also  be  compelled  to  show,  that 
under  Moissan  this  method  has  finally  found  its  way  into  the 
most  renowned  Chemical  Laboratory  of  Paris — and  this  fact 
is  specially  pointed  out  in  a  formal  report  of  the  entire 
Chemical  Section  of  the  Academy  of  Sciences  of  Paris, 
which  granted  a  prize  in  accordance  with  this  report,  in 
December,  1900 — when  as  a  matter  of  fact  even  the  simple 
formula  for  this  calculation  is  not  known  in  that  Laboratory, 
so  that  all  values  calculated  are  fifty  per  cent  too  high! 

We  shall  therefore  have  to  show  this  calculation  in  detail, 
by  applying  it  to  our  weighings  of  the  silver  dollars. 

The  Constant  Errors. 

We  shall  then  also  see  clearly  that  this  method  does  not 
furnish  any  clew  to  the  limit  of  the  constant  errors  of  the 
chemical  work,  or  any  indication  of  the  real  error  com- 
mitted— in  which  opinion  chemists  have  used  it — but  simply 
gives  mathematical  expression  of  the  degree  of  concordance 
of  the  experimental  determinations  made. 

It  would  indeed  be  delightful  to  possess  some  mathe- 
matical process  by  which  erroneous  chemical  work  could  be 
corrected. 

Chemists  evidently  thought  that  the  calculation  of  the 
probable  error  shows  them  at  least  how  near  they  came  to 
the  truth. 

That  this  absurd  fallacy  could  become  accepted  so  widely 
in  the  chemical  world  is  very  deplorable;  but  that  chemists, 
like  Moissan,  do  not  even  take  the  trouble  to  use  the  true 
formula,  is  almost  incredible;  unhappily  it  is  true 

Two  Common  Errors. 

We  shall  next  find,  that  two  additional  and  very  grave 
errors  are  commonly  committed  in  the  so-called  reductions 
of  experiments  or  observations  by  chemists  and  other  sci- 
entists, and  which  errors  must  be  avoided  to  obtain  true 
results  of  atomic  weights. 


THE    ERRORS    OF    PRECISION. 


We  refer  to  the  habit  of  calculating  decimals  beyond  the 
limit  of  actual  precision,  and  to  the  use  of  auxiliary  data 
which  are  not  true. 

Suppose  I  can  distinguish  only  the  fiftieth  of  an  inch,  by 
sight,  can  I  then  pretend  to  accurately  measure  to  the 
thousandths?  And  again,  if  I  weigh  to  the  centigramme 
because  my  balance  requires  at  least  half  a  centigramme  of 
overweight  to  turn  distinctly,  how  can  I  pretend  to  know 
the  tenth  of  a  milligramme  by  weighing  with  that  balance? 

And  if,  for  calculating  the  cost  of  a  given  number  of 
things,  I  use  a  false  value  per  unit,  will  not  my  calculated 
price  be  false  also,  and  therefore  worthless? 

We  shall  see,  that  also  this  kind  of  error  is  constantly 
committed  by  chemists,  in  their  " adopting"  as  true  some 
determination  made  by  men  in  authority,  without  exacting 
proper  proof  that  the  authority  did  commit  no  error  in  his 
work. 

Our  Course  of  Training. 

When  we  shall  have  become  familiar  with  the  reality  of 
these  errors,  and  shall  have  learnt  how  universally  these 
very  errors  have  been  and  are  being  committed  by  chemists 
in  atomic  weight  determinations,  we  will  have  completed 
that  introductory  course  of  training  necessary  to  the  begin- 
ning of  the  study  of  the  chemical  and  simple  mathematical 
methods  that  must  be  used  to  obtain  the  true  and  absolute 
atomic  weights  of  the  chemical  elements. 

We  shall  now  present  each  of  these  common  methods 
and  their  common  errors  in  the  simplest  way  possible,  by 
actual  examples,  and  with  the  necessary  details. 

In  order  that  this  preliminary  work  may  not  become  too 
tiresome,  we  shall  freely  call  spade  a  spade,  independent  of 
the  hand  that  uses  it. 

Our  object  being  to  establish  truth,  we  shall  not  com- 
promise with  error,  even  if  that  error  be  practiced  by  men 
in  the  highest  stations. 


THE    MEANT   WEIGHT   OF   A   SILVER   DOLLAR.  J 

II.     THE  MEAN  WEIGHT  OF  A  SILVER  DOLLAR. 

In  order  to  test  the  value  of  the  mean,  I  have,  on  ten 
different  days,  taken  a  roll  of  twenty  silver  dollars  at  the 
bank— thus  obtaining  two  hundred  single  silver  dollars  as 
they  were  in  circulation  during  the  first  four  months  of  1901. 

Each  coin  was  separately  weighed  exactly  to  the  centi- 
gramme and  the  mean  or  average  weight  was  calculated,  as 
well  as  the  so-called  probable  error  of  this  mean.  This 
probable  error  we  shall  explain  later  on  when  we  shall  begin 
the  study  thereof;  pp.  11-20. 

It  will  not  be  necessary  here  to  give  the  individual  weigh- 
ings except  for  the  heaviest  and  lightest  coin  of  each  series 
of  twenty,  that  is,  the  extremes.  It  is  also  important  to 
notice  the  range  or  difference  between  these  extremes. 

We  may  here  add,  that  the  extremes  and  range  furnish  a 
true  indication  of  the  practical  concordance  of  any  series 
of  determinations  of  any  single  value.  We  shall  see  further 
on,  that  this  is  all  the  probable  error  can  do. 

Determination  of  the  Weight  of  a  Silver  Dollar. 


1901. 

No. 

Highest. 

L.owest. 

Range. 

Mean. 

Prob.  Error. 

Jan'y    15, 

20 

26.69 

25.98 

0.71 

26.40 

3-2Cgr. 

"      25, 

20 

6.7I 

6.10 

.61 

.48 

2.6 

Feb'y     8, 

20 

6.77 

5-92 

•85 

•43 

4-5 

"       27, 

2O 

6.76 

5-84 

.92 

•36 

4.2 

March  n, 

20 

6.72 

5-87 

•85 

.40 

3-6 

"       25, 

20 

6.7I 

5.86 

•85 

•31 

4-i 

April      4, 

20 

6-73 

5-95 

.7S 

•5i 

3-o 

"       15, 

20 

6.7I 

6.02 

.69 

•37 

3-7 

"       25, 

20 

6.74 

5-73 

I  .01 

.28 

4-8 

May        3, 

2O 

6.70 

5-65 

1.05 

•33 

4-2 

Means,  20      26.72       25.89      0.83       26.39        3-7 

Absol.  extremes,    26.77      25.65       1.12 

It  will  be  noticed  that  the  mean  weight  of  the  silver  dollar 
in  any  one  roll  of  twenty  coins  varies  from  26.28  to  26.51 
grammes  or  23  centigrammes ;  that  is  nearly  a  quartet  of  a 
gramme,  or  almost  one  per  cent  of  the  mean  weight  of  the 
two  hundred  single  silver  dollars  weighed. 


THE    ERRORS    OF    PRECISION. 


The  range  in  any  one  series  of  twenty  silver  dollars 
varies  from  61  to  105  centigrammes,  averaging  83  centi- 
grammes for  each  series  of  twenty  coins. 

Mean  Weight  not  True  Weight. 

But  can  we  for  a  moment  accept  the  mean  weight  of  the 
two  hundred  silver  dollars  actually  weighed  as  the  true 
weight  of  a  United  States  Silver  Dollar?  Is  the  mean  26.39 
grammes  actually  determined  from  two  hundred  weighings, 
the  true  weight  of  our  silver  dollar?  Is  the  mean  value  of 
the  means  of  ten  series  of  twenty  determinations  each  the 
true  weight? 

Most  assuredly  not;  nor  would  we  obtain  that  true  weight 
by  indefinitely  continuing  this  work  of  actual  weighing  the 
coins  in  circulation. 

We  have  here  a  plain  case  showing  the  fallacy  of  accept- 
ing the  mean  value  as  the  true  value,  even  if  determined  by 
ten  series  of  twenty  experimental  determinations  each. 

Effect  of  Wear.    Abrasion. 

In  this  case  the  cause  of  the  error  of  the  mean  is  well 
understood :  it  is  due  to  the  wear  or  abrasion  produced  by 
circulation,  and  this  is  not  equal  for  the  different  coins  but 
varies  according  to  the  actual  handling  each  coin  has  under- 
gone since  leaving  the  mint. 

And  the  amount  of  this  abrasion  will  roughly  depend  on 
the  length  of  time  the  coin  has  been  in  circulation,  which 
time  is  determined  by  the  year  of  coinage  stamped  on  each 
coin. 

It  would  be  exceedingly  interesting  to  give  our  full  data 
of  observation  on  this  subject,  an  account  of  its  importance 
on  the  common  scientific  practice  of  taking  the  mean  value 
as  the  true  value ;  but  our  space  will  allow  only  the  following 
general  points  to  be  stated: 

Frequency  in  Circulation. 

The  frequency  of  coin  of  any  given  year  is  most  remark- 
ably different,  and  not  at  all  equal,  as  might  have  been 
supposed. 


THE    MEAN*    WEIGHT   OF    A   SILVER   DOLLAR. 


The  200  silver  dollars  weighed  bear  as  years  of  coinage 
numbers  from  1878  to  1899,  extending  over  22  years.  Sixty 
one  of  these  coins  bore  one  of  the  three  years  1889,  1890  and 
1891 ;  their  mean  year  of  coinage  therefore  is  1890.  Sixty 
eight  of  the  200  silver  dollars  weighed  were  coined  in  the 
six  years  from  1879  *°  J884  inclusive. 

In  the  nine  years  here  specified,  129  of  the  200  silver 
dollars  were  coined,  leaving  only  71  coins  to  the  13  years 
not  specified. 

Roughly  speaking  we  may  say  that  in  the  number  of  coins 
in  circulation  the  three  years  1889-1891  and  the  six  years  1879 
to  1884  and  aH  the  other  thirteen  years  not  herein  included 
have  furnished  a  nearly  equal  number  of  silver  dollars, 
namely  respectively  61/68  and  71  for  each  of  these  groups, 
This  gives  about  20,  10  and  5  for  each  single  year  of  the 
groups  of  years  specified. 

This  is  a  much  greater  variation  in  frequency  than  could 
have  been  anticipated. 

The  Mean  a  Lower  Limit. 

Since  evidently  abrasion  lowers  the  weight  of  a  coin  in 
circulation,  every  weight  of  a  coin  is  below  its  true  legal 
weight  and  every  mean  will  therefore  also  necessarily  be 
below  the  weight  fixed  by  law  for  the  silver  dollar  coin 
(within  the  tolerance). 

In  this  case,  the  mean  weight  of  the  actual  coins  in  circu- 
lation can  never  furnish  the  true  weight  of  the  silver  dollar. 

The  true  weight  of  the  silver  dollar  at  the  time  of  coinage 
is  evidently  the  mean  weight  in  actual  circulation  increased 
by  the  loss  due  to  abrasion  in  circulation. 

In  other  words,  the  actual  weight  determined  by  weighing 
the  coins  in  circulation,  and  any  means  of  such  weighings, 
give  only  a  lower  limit*  of  the  true  weight  of  the  coin. 

Amount  of  Abrasion. 

Now,  the  68  silver  dollars  coined  between  1879  and  I&H 
gave  the  mean  weight  26.288;  their  mean  year  of  coinage 
is  i88i>£. 

*  On  that  fact  rests  our  method  used  in  the  True  Atomic  Weights,  1894. 


THE    ERRORS    OF    PRECISION. 


The  61  silver  dollars  coined  between  1889  and  1891  gave  a 
mean  weight  of  26.405  grammes;  1890  is  their  mean  year  of 
coinage. 

The  mean  weight  of  these  61  dollars  exceeds  the  mean 
weight  of  the  68  which  are  8^  }7ears  older,  by  0.117 
grammes;  hence  the  abrasion  was  at  the  rate  of  0.137  in  the 
ten  years,  between  1880  and  1890. 

Calculated  Weight  of  New  Coin. 

If  we  were  permitted  to  assume  the  same  amount  of 
abrasion  during  the  ten  years  from  1890  to  1900,  we  would 
fix  the  mean  weight  of  a  silver  dollar  at  the  mint  in  1900, 
before  entering  into  circulation,  at  26.54  grammes,  namely, 
to  the  mean  weight,  26.405  for  1890  we  would  add  the 
abrasion  0.137  found  for  ten  years  in  the  eighties. 

Since  now  the  abrasion  of  new  coins  is  not  necessarily 
the  same  per  year  as  the  abrasion  for  older  coins  that  have 
already  lost  the  most  prominent  points  by  abrasion,  this 
calculated  weight  of  26.54  as  the  mean  weight  of  a  new 
silver  dollar  coined  at  our  mints  in  1900  is  only  a  lower  limit 
itself. 

In  that  mean  weight  the  tolerance  will  figure  as  an  equally 
possible  variation  above  and  below  the  mean 

Testing  the  Result. 

I  was  unable  to  secure  at  banks  and  even  at  the  U.  S. 
Subtreasury  in  the  City  of  St.  Louis  any  silver  dollars  that 
had  not  yet  been  in  public  circulation. 

But  the  legal  weight  was  stated  to  be  412  .50  grains,  which 
is  equivalent  to  26.730  grammes.  Hence  we  see  that  an 
estimate  from  the  mean  weights  is  still  too  low  by  19  centi- 
grammes. 

Even  the  means  of  the  highest  observed  is  still  one  centi- 
gramme below  the  legal  standard. 

But  in  four  of  the  ten  lots  of  twenty  silver  dollars,  the 
heaviest  exceeded  by  a  few  centigrammes  the  legal  standard. 

It  is  well  understood  that  it  is  impossible  to  produce 
coins  of  the  exact  weight  fixed  by  law;  a  practical  limit  is 
assigned,  called  the  "tolerances'* 


THE  PROBABLE  ERROR  OF  THE  ME  AX. 


Not  having  been  able  to  obtain  new  silver  dollars,  even 
at  the  United  States  Subtreasury  in  St.  Louis,  I  cannot 
determine  the  value  of  the  actual  tolerance  .practiced  in 
coining  our  silver  dollars. 

A  single  stray  new  silver  dollar  of  1901,  a  rara  avis  in  the 
West,  was  just  trapped  and  found  to  weigh  26.77  grammes, 
which  is  4  centigrammes  above  legal  weight. 

Estimate  from  Quarters. 

But  I  succeeded  in  getting  absolutely  new  quarters,  at  the 
Boatmen's  Bank.  The  mean  weight  was  6.250  grammes; 
the  heaviest  6.30,  the  lightest  6.20,  showing  a  tolerance 
either  way  of  5  centigrammes. 

If  we  could  be  permitted  to  take  the  new  quarters  as  one 
fourth  of  a  new  silver  dollar,  the  latter  would  weigh  25 .000 
grammes  and  show  a  greatest  tolerance  of  20  centigrammes 
either  way. 

But  this  mean  is  i  .73  grammes  below  the  legal  standard; 
accordingly  we  must  suppose  that  the  legal  weight  of  a 
quarter  is  considerably  less  than  the  fourth  of  the  legal 
weight  of  the  silver  dollar. 

This  shows,  how  complex  even  so  simple  a  case  as  the 
experimental  determination  of  a  common  silver  dollar  coin 
becomes  when  tried,  without  reference  to  the  law  governing 
the  coinage. 

Now,  chemists  have  tried  to  experimentally  determine  the 
weight  of  the  atoms — without  reference  to  the  general  Laws 
of  Nature.  No  wonder  they  made  a  mess  of  it,  and  now 
want  to  settle  it  by  vote. 

III.    THE  PROBABLE  ERROR  OF  THE  MEAN. 

Scientists  hold,  that  the  probable  error  of  a  single 
observation  is  at  such  a  distance  from  the  mean  that  it  is  an 
even  wager  or  an  even  chance  for  a  single  actual  observation 
to  fall  within  this  distance  or  beyond  it. 

In  other  words,  if  we  arrange  all  observed  values  in  the 
order  of  their  magnitude,  one  half  of  all  should  fall  nearest 
the  mean  and  be  not  more  distant  therefrom  than  is  measured 
by  the  probable  error  of  a  single  observation. 


THE    ERRORS    OF    PRECISION. 


The  probable  error  of  the  mean  of  a  number  of  observa- 
tions is  obtained  by  dividing  the  probable  error  of  a  single 
observation  by  the  square  root  of  the  total  number  of 
observations. 

Thus,  if  4  observations  have  been  made,  all  with  equal 
care,  the  probable  error  of  the  mean  will  be  only  one  half 
of  the  probable  error  of  a  single  observation ;  for  16  equally 
careful  observations,  the  probable  error  of  the  mean  will  be 
only  one  fourth  of  the  probable  error  of  a  single  observation 
or  determination. 

In  other  words,  mathematicians  have  demonstrated,  that 
the  probable  error  of  the  mean  diminishes  as  the  square 
root  of  the  number  of  determinations  increases. 

In  this  circumstance  lies  the  temptation  to  the  belief  that 
we  need  only  increase  the  number  of  determinations  to  get 
nearer  the  truth. 

That  is,  if  this  mean  really  were  the  true  value.  But  we 
have  seen  the  mean  is  not  necessarily  the  true  value. 

Systematic  and  Constant  Errors. 

We  cannot  here  enter  upon  this  rather  difficult  discussion; 
we  need  only  say,  that  all  this  very  nice  theory  is  rudely  des- 
troyed by  the  actual  existence  of  systematic  and  constant 
errors,  which  in  the  above  mathematical  theory  are  supposed 
to  be  absent  or  to  have  been  determined. 

This  is  exactly  as  in  the  laws  of  the  pulley  in  physics ,- 
very  simple,  easily  understood,  if  friction  and  the  stiffness 
of  cordage  are  supposed  not  to  exist;  but  we  know,  that 
these  great  influences  can  not  be  overlooked  by  us,  because 
they  constitute  great  facts  in  nature. 

Calculation  of  Probable  Error. 

But  since  this  method  is  in  actual  use,  we  shall  have  to 
give  the  method  of  calculation  of  the  probable  error  of  the 
mean  of  any  number  of  determinations. 

If,  at  any  time,  the  probable  error  of  a  single  determina- 
tion be  wanted,  we  can  obtain  it  by  multiplying  the  probable 
error  of  the  mean  by  the  square  root  of  the  total  number  of 
determinations,  as  practically  stated  above. 


THE  PROBABLE  ERROR  OF  THE  MEAX.          13 

The  manner  of  calculating  the  probable  error  of  the  mean 
is  quite  simple.  Having  calculated  the  mean  of  all  deter- 
minations, we  find  the  differences  between  this  mean  and 
every  single  determination.  We  square  each  one  of  these 
differences,  and  take  the  sum  of  these  squares. 

Next  we  multiply  the  number  of  determinations  by  the 
next  lower  number.  The  sum  of  the  squares  is  divided  by 
this  product. 

Two-thirds  of  the  square  root  of  the  quotient  thus 
obtained  is  the  probable  error  of  the  mean. 

It  may  be  necessary  to  give  an  example  in  full  detail  of 
this  calculation  of  the  probable  error  of  a  mean.  Let  us 
take  the  20  silver  dollars  weighed  on  April  4,  1901. 

The  year  of  coinage  of  each  silver  dollar  and  its  weight 
(in  grammes  and  centigrammes)  is  given  in  the  first  two 
columns. 

The  mean  26.51  gives  the  difference  expressed  in  centi- 
grammes in  the  next  column.  The  fourth  column  gives  the 
square  of  each  of  these  differences. 


ear. 

Weight. 

Difference. 

Square. 

*8o 

25-95 

56 

3136 

82 

26.24 

27 

729 

90 

.24 

27 

729 

89 

•37 

H 

196 

78 

•39 

12 

144 

87 

.40 

II 

121 

89 

•45 

6 

36 

89 

•45 

6 

36 

84 

.48 

3 

9 

80 

•51 

0 

0 

97 

•59 

8 

64 

99 

•59 

8 

64 

96 

.65 

H 

196 

99 

•65 

14 

196 

97 

.66 

15 

225 

83 

.68 

17 

289 

90 

.69 

18 

324 

99 

•71 

20 

400 

91 

.72 

21 

441 

91 

•73 

22 

484 

Mean   26.51 

Sum 

7821 

14  THE    ERRORS    OF    PRECISION. 

The  sum  of  these  twenty  squares  foots  up  to  7821.  The 
20  observations  multiplied  by  the  next  lower  number  (here 
19)  gives  \hQ#roduct  380. 

Dividing  the  sum  7821,  by  this  product,  380,  we  obtain 
the  quotient  20.58. 

Extracting  the  square  root  of  this  quotient  we  obtain  4 .54. 

Subtracting  one  third  herefrom,  there  remains  3  .03  as  its 
two-thirds  j  which  therefore  is  the  probable  error  of  the  mean 
of  the  twenty  silver  dollars,  in  centigrammes.  We  drop  the 
second  decimal  as  unreliable. 

The  operations  involved  in  this  calculation  of  the  prob- 
able error  of  the  mean  are  all  simple  enough — although 
quite  tedious  if  a  large  number  of  such  calculations  has  to 
be  effected. 

Shall  we  use  this  Error? 

If  the  so-called  probable  error  possesses  any  scientific 
value,  it  will  then  be  proper  to  calculate  the  same.  But 
if  the  value  so  obtained  is  practically  worthless  it  would  be 
worse  than  pedantry  to  carry  out  these  calculations. 

If  the  so-called  probable  error  of  the  mean  should  convey 
a  false  idea,  or  have  been  obtained  in  any  case  under  condi- 
tions which  prohibit  this  mode  of  calculation,  then  false 
data  of  fact  would  be  foisted  upon  science,  and  a  fraud 
would  be  committed. 

So  far  as  science  is  concerned,  the  fraud  would  exist, 
even  though  the  person  guilty  be  not  aware  thereof — on 
account  of  lack  of  understanding. 

In  science,  there  can  be  no  excuse  given  for  stating  a 
false  fact  or  a  false  result  obtained  by  using  a  false  method 
or  process,  whether  of  practical  laboratory  work  or  of 
calculation. 

It  is  the  duty  of  the  scientist  to  test  the  methods  of 
practice  and  of  calculation  which  he  employs.  If  he  con- 
tinues to  employ  them  after  they  have  been  shown  to  be 
erroneous,  he  is  surely  guilty  of  committing  a  scientific 
fraud  in  using  them. 


THE  PROBABLE  ERROR  OF  THE  MEAN.          15 

Condition  by  Number. 

Now.  first  of  all,  this  method  of  calculation  presupposes 
that  the  number  of  observations  or  determinations  is  large. 
In  our  case  it  is  20;  that  is  about  as  low  as  may  be  permitted. 

But  in  the  applications  of  this  method  made  for  the 
calculation  of  the  atomic  weights,  generally  but  few  data  or 
determinations  are  at  hand.  In  our  record  following  this 
number  will  be  stated  in  every  case.  It  is  generally  under 
ten,  mostly  under  five. 

In  one  of  the  most  favorable  cases,  that  of  lead,  we  find 
the  number  of  determinations  to  be  9-4-3-6-7-3-3-3-4-6-4-4 
in  the  order  in  which  they  are  given  in  the  Smithsonian 
Constants  of  Nature,  1897,  pp.  127  to  131. 

The  total  aggregates  56  determinations  for  the  12  series; 
that  is  an  average  of  4%  to  the  series. 

The  highest  individual  number  of  determinations  is  9; 
but  this  should  have  been  counted  as  two  series,  of  6  and  3 
determinations. 

Without  going  beyond  this  point,  we  must  therefore  con- 
demn as  scientific  frauds  all  the  probable  errors  given  in  the 
Smithsonian  work  specified,  because  the  method  of  calcula- 
tion is  applied  in  all  these  cases  under  an  insufficiency  of 
the  number  of  determinations  made. 

That  the  probable  error  is  calculated  to  three  and  four 
decimals  aggravates  the  scientific  fraud  many  fold. 


Condition  by  Probability. 

In  the  second  place,  every  one  entitled  to  use  this  method 
of  the  calculation  of  the  probable  error  is  required  to  know 
that  the  actual  differences  have  to  be  distributed  according 
to  the  law  of  probability,  and  symmetric  to  each  side  of  the 
mean. 

This  condition  is  nearly  always  violated  in  the  applica- 
tions made  in  calculating  the  probable  error  of  the  mean 
values  of  the  atomic  weight  determined  by  any  one  process 
in  any  one  series.  In  fact,  no  chemist  seems  to  be  aware  of 
this  limitation. 


l6  THE    ERRORS    OF    PRECISION. 

I  have  pointed  out  one  of  the  most  flagrant  cases  of  the 
multitude  committed  by  Professor  Ostwald  of  Leipzig  under 
the  highest  pretentions  to  scientific  precision.  See  my 
"True  Atomic  Weights,"  pp.  43-44;  1894. 

In  the  entire  big  book  of  the  "Constants  of  Nature," 
issued  in  1897,  by  the  Smithsonian  Institution,  there  is  not 
half  a  dozen  cases  among  the  hundreds  given,  in  which  this 
essential  condition  has  not  been  violated. 

Conditions  were  Disregarded. 

Accordingly,  practically  speaking,  all  the  calculated 
values  of  the  probable  error  of  the  mean  values  of  atomic 
weight  determinations  published  up  to-date  in  all  scientific 
works  on  atomic  weights  issued,  have  been  obtained  in  total 
disregard  of  these  two  fundamental  conditions  which  are 
pre-requisite  to  the  application  of  this  mode  of  calculation. 

In  the  determinations  of  the  atomic  weight  of  boron 
made  in  the  laboratory  of  Moissan  at  Paris,  recommended 
by  him  and  his  section  of  chemistry  to  the  Academy  of 
Sciences  for  a  prize  which  was  granted  in  December,  1900, 
the  study  of  the  probable  error  was  specially  accentuated ; 
and  yet  neither  the  chemist  Moissan,  nor  his  endorsing 
colleagues  know  the  formula  for  the  calculation  of  that 
probable  error,  having  omitted  the  coefficient  %;  all  pre- 
tended values  given  and  studied  (discute)  and  crowned  by 
the  Academy  are  only  50  per  cent  too  high.  See  Annales  de 
Chimie,  etc.,  T.  18,  p.  363;  1899,  where  the  formula  used  is 
printed  as  "formule  connu." 

Conditions  Applied  by  us. 

Let  us  apply  these  conditions  to  the  calculation  of  the 
probable  error  of  the  mean  weight  of  the  twenty  silver 
dollars  weighed  by  us  on  April  4,  1901.  See  page  13. 

The  number  of  determinations,  being  20,  is  just  passable. 

The  differences  are  quite  evenly  distributed  about  the 
mean,  though  it  must  be  noted  that  the  difference  for  the 
lightest  coin  is  excessive. 


THE  PROBABLE  ERROR  OF  THE  MEAN.  17 

The  probable  error  of  3  centigrammes  would  therefore 
be  accepted  as  reasonably  well  established. 

But  even  this  fairly  authorized  probable  error  possesses 
no  practical  value  in  this  question,  the  determination  of  the 
weight  of  a  silver  dollar. 

In  the  record  of  the  ten  series  of  weighings  (p.  7)  we  find 
the  probable  errors  to  range  from  2.6  to  4.8  centigrammes, 
while  the  mean  weights  actually  run  from  26.28  to  26.51,  that 
is  over  23  centigrammes,  and  while  all  these  means  are  noto- 
riously below  the  true  weight  on  account  of  abrasion. 

Let  us  check  this  case  by  the  condition  of  an  even  ivager, 
calculating  the  corresponding  probable  error  of  a  single 
determination  or  silver  dollar. 

The  total  number  being  20,  the  square  root  of  which  is 
4.47  (for  which  we  can  take  43*0  we  shall  obtain  the  prob- 
able error  of  a  single  dollar  by  multiplying  the  probable 
error  of  the  mean  3  by  this  number  4^.  We  obtain  14  cen- 
tigrammes or  0.14  grammes. 

Counting,  on  the  list  above  given  (p.  13)  the  number  of 
dollars  weighing  between  14  centigrammes  less  and  more 
than  the  mean  of  26.51,  that  is,  between  26.37  and  26.65,  we 
find  eleven,  instead  of  exactly  half  the  total  number.  Since 
it  so  happens  that  the  weight  26.65  occurs  twice,  we  are  per- 
fectly satisfied  as  to  the  distribution  of  these  silver  dollars 
according  to  the  law  of  probability,  at  least  on  this  most 
essential  condition,  so  readily  tested. 

All  Published  Probable  Errors  are  False. 

But  this  test  of  applicability  being  unknown  to  chemists, 
they  have  never  applied  it  in  their  calculations.  If  applied, 
it  would  condemn  almost  all  the  calculations  of  the  probable 
error  made  by  chemists. 

From  whatever  side  we  view  the  probable  error  of  the 
mean  calculated  by  chemists,  we  must  condemn  it  as 
obtained  in  absolute  ignorance  of  the  conditions  imposed 
by  science.  Hence  the  results  are  not  only  worthless,  but 
they  are  false  and  fraudulent. 


l8  THE    ERRORS    OF    PRECISION. 


The  Double  Distilled  Fraud. 

It  follows  without  saying  that  all  estimates  of  the  scien- 
tific value  of  series  of  atomic  weight  determinations  depend- 
ent upon  the  minuteness  of  this  so-called  probable  error  are 
not  only  double  distilled  frauds,  but  the  impertinent,  arro- 
gant imposition  of  an  ignorant  mechanical  calculator  who 
blindly  applies  a  mathematical  method  he  does  not  under- 
stand to  the  work  of  chemists  he  does  not  comprehend.  We 
refer  to  the  author  of  the  Constants  of  Nature,  which  are 
neither  constant  nor  of  nature. 

I  shall  not  go  into  further  particulars  at  this  point  by 
giving  striking  instances  of  such  absurd  judgements  pro- 
nounced on  work  done  by  American  Chemists,  but  shall 
point  out  a  few  glaring  instances  as  we  go  along  in  the  sum- 
mary of  the  atomic  weight  determinations  made  during  the 
nineteenth  century. 

The  Law  of  Probability. 

As  to  the  Laiv  of  Probability  here  referred  to,  I  may  be 
permitted  to  state,  that  the  same  has  been  independently 
established  by  me  in  a  strictly  experimental  manner  as  pub- 
lished in  my  u  School  Laboratory  of  Physical  Science,  vol. 
II,  pp.  28-38;  Iowa  City,  1872,"  and  also  in  my  "  Rainfall 
Laws,  reduced  from  Twenty  Years  of  Observarion,"  pp.  43- 
56,  Washington,  D.  C.,  Weather  Bureau,  1893. 

Fully  half  a  million  experiments  were  made  by  my  stu- 
dents. These  experiments  completely  established  my  sim- 
ple and  practical,  graphic  method  of  applying  the  proba- 
bility curve,  which  otherwise  had  only  been  accessible  by 
means  of  difficult  methods  of  higher  mathematics. 

This  remark  is  here  appended  to  prevent  improper 
inferences  and  not  unlikely  insinuations. 

All  Dice  are  Loaded. 

How  sensitive  some  very  common  operations  are  to 
minute  influences  readily  overlooked  by  us,  we  may  see  in 
the  throwing  of  dice. 


THE  PROBABLE  ERROR  OF  THE  MEAN.          19 

A  series  of  26,602  casts  of  12  dice  each  (Prof.  Weldon's 
experiment)  is  lately  reported  by  Professor  Karl  Pearson  of 
University  College,  London,  in  the  Philosophical  Magazine, 
vol.  50,  p.  168;  July,  1900.  The  total  number  of  "fives"  and 
"  sixes"  thrown  was  106,602.  Thus  the  fact. 

The  total  number  of  dice  thrown  was  12  times  26,602  or 
315,672;  hence  the  actual  ratio  for  the  fives  and  sixes  was 
106,602  divided  by  315,672  which  150.3377. 

But  the  fives  and  sixes  mark  one  third  of  the  six  faces  of 
dice,  and  should  therefore  have  occurred  one  third,  that  is 
0.3333  times  of  all,  for  strictly  even  chances. 

The  fives  and  sixes  actually  thrown  exceed  their  theo- 
retical probability  (of  the  even  chance)  by  o  .0044,  that  is  by 
44  on  10,000.  This  corresponds  to  our  " analytical  excess" 
in  the  following. 

False  Science  from  False  Facts  and  False  Tools. 

Suppose  one  of  our  modern  "exact  scientists"  proceeds 
to  establish  the  law  of  probability  by  throwing  of  dice,  and 
takes  this  mere  fact  of  0.3377  as  the  true  probability,  would 
he  not  get  up  some  very  fine  science  ? 

He  would,  in  that  case,  overlook  the  fundamental  error 
involved  in  the  fact  that  dice,  marked  as  they  are,  cannot 
give  a  strictly  even  chance,  but  necessarily  favor  the  high 
throws,  that  is  the  fives  and  sixes. 

Why?  Under  the  five  depressions  we  have  only  two, 
under  the  six  small  holes  only  one ;  in  other  words,  the  best 
of  dice,  by  the  method  of  making,  are  lightened  at  the  faces 
with  five  and  six  depressions  in  comparison  to  the  opposite 
faces,  which  thus  are  relatively  " loaded"  because  a  mere 

trifle  of  substance  less  has  been  removed. 

.*-• 

Nature  can  not  be  Suppressed. 

Now,  the  force  of  gravity  cannot  be  suppressed — it  points 
out  with  unerring  hand  this  trifling  amount  of  matter.  So 
nature  always  points  out  what  exact  scientists  overlook. 

And  thus  we  would  "falsely "  condemn  the  true  proba- 
bility of  an  even  chance  if  we  tried  to  prove  an  abstract 


2O  THE    ERRORS    OF    PRECISION. 

principle  by  a  mere  experiment — in  which  we  overlook 
one  missing  condition,  the  lack  of  absolute  equality  in  fact. 
This  error  of  common  dice  came  to  our  knowledge  when 
making  experiments  on  the  law  of  probability  more  than 
thirty  years  ago. 

The  Exact  Scientist  should  be  Tested  First. 

When  we  try  to  test  Nature,  let  us  not  forget  to  test 
ourselves  and  our  toolsyfrs/. 

When  making  our  extended  experiments  on  the  laws  of 
probability  thirty  years  ago,  we  found  it  impossible  to  get 
exactly  equal  balls  for  the  urn  from  which  the  draws  were 
made;  we  did,  however,  not  ascribe  these  errors  to  the  laws 
of  probability,  but  to  the  imperfections  of  our  own  means 
at  hand. 

The  Greatest  False  Scientist. 

i — - 

If  modern  chemists  did   not  suppose  Stas   perfect,   the 

atomic  weights  of  modern  chemistry  would  not  present  the 
mysterious  muddle  they  do. 

Our  modern  chemists,  under  the  leadership  of  Stas,  have 
corrupted  chemical  science  by  their  assumption  of  a  perfec- 
tion and  exactness  in  experimentation  that  existed  necessarily 
only  in  their  own  imagination ;  as  a  result,  the  atomic 
weights  actually  in  use  for  years  are  all  false,  contrary  to 
nature,  as  we  shall  prove  beyond  the  possibility  of  a  doubt. 
X 

IV.    THE  CONSTANT  ERROR  OF  THE  MEAN. 

But  if  we  cannot  use  the  mean  of  a  large  number  of 
simple  weighings  of  actual  coins  in  circulation  as  the  true 
value  of  such  a  coin,  how  dare  we  assume  that  the  mean 
value  of  a  very  few  determinations  of  the  atomic  weight  of 
a  chemical  element  will  give  us  its  true  value,  or  that  we 
shall  approach  it  more  closely  by  taking  the  mean  of  the 
mean  values  of  a  few  series  of  such  determinations? 

The  unavoidable  errors  in  the  different  chemical  pro- 
cesses made  use  of  in  these  determinations  are  much  more 


THE  CONSTANT  ERROR  OF  THE  MEAN*.          21 

difficult  to  estimate  and  comprehend  than  the  mere  abrasion, 
influenced  by  more  or  less  rapid  circulation  and  by  peculi- 
arities in  the  frequency  of  certain  coinage  years  over  others ; 
but  they  are  not  less  real  than  errors  due  to  abrasion. 

The  unavoidable  errors  affecting  the  different  chemical 
processes  are,  however,  not  all  working  one  way,  as  it  is 
necessarily  in  the  abrasion  of  a  coin  making  actual  weight  in 
circulation  always  lower  than  its  original  and  true  legal 
weight. 

Lower  and  Higher  Limits. 

Indeed,  for  many  chemical  processes  we  have  means  of 
knowing  whether  they  are  giving  the  atomic  weight  too 
high  or  too  low.  See  Rule  of  Berzelius,  p.  3. 

Accordingly,  in  such  cases  we  know  whether  we  obtain 
a  higher  or  a  lower  limit  of  the  atomic  weight  found  by  the 
chemical  operation  employed. 

This  will  enable  us  to  fix  a  higher  and  a  lower  limit  of  the 
atomic  weight  sought,  but  in  no  case  is  the  exact  or  absolute 
atomic  weight  thus  determined ;  for  we  have  no  chemical 
means  of  ascertaining  the  exact  amount  of  the  excess  or 
deficiency  due  to  the  chemical  operations  used. 

The  special  example  here  considered,  namely  the  experi- 
mental determination  of  the  true  weight  of  a  given  coin  by 
the  process  of  actually  weighing  the  coin,  at  hand,  shows  in 
a  striking  manner  the  insufficiency  of  mere  empirical  or 
experimental  work  in  the  determination  of  any  given  quan- 
tity actually  occuring  in  nature  or  commerce. 

Laboratory  Work  Alone  not  Enough. 

The  determination  of  the  atomic  weight  of  a  chemical 
element  being  a  much  more  complicated  process,  involving 
not  only  weighings  but  also  chemical  operations  that  bring 
the  material  operated  upon  into  chemical  circulation,  will 
now  be  understood  to  require  something  more  than  mere 
laboratory  work  and  weighings,  and  even  much  more  than 
the  calculation  of  the  probable  error  of  their  mean  value. 


24  THE   ERRORS    OF    PRECISION. 


approaches  the  year  in  which  the  weighings  are  actually 
made. 

Even  in  the  case  of  coins,  we  remain  ignorant  of  the 
exact  conditions  of  this  error,  depending  on  the  rapidity 
and  character  of  actual  circulation. 

This  is  precisely  the  condition  which  modern  chemistry 
presents  to-day  in  its  record  of  atomic  weight  determina- 
tions. The  form  in  which  these  conflicting  results  of 
experiment  are  usually  presented  fails  to  convey  a  proper 
appreciation  of  the  magnitude  of  these  differences. 

As  it  is  most  important  at  the  outset  of  this  investigation 
to  have  a  proper  understanding  of  the  actual  errors  prevail- 
ing, we  shall  give  the  necessary  details  for  the  most  valuable 
element — gold. 

V.     ACTUAL  ERRORS  OF  THE  MEAN. 

That  the  mean  of  a  series  of  atomic  weight  determina- 
tions is,  de  facto,  affected  with  quite  large  constant  errors 
(constant  for  each  series  or  process  used)  can  be  seen  by  the 
examination  of  any  actual  chemical  set  of  determinations. 

To  make  the  fact  convincing,  we  select  the  very  noted 
work  of  Mallet  on  the  atomic  weight  of  gold. 

This  most  noted  chemical  work  on  the  atomic  weight  of 
gold  was  done  by  Professor  J.  W.  Mallet  of  the  University 
of  Virginia,  and  first  published  in  the  Philosophical  Trans- 
actions of  the  Royal  Society  (London)  for  1889. 

Through  the  personal  courtesy  of  the  distinguished 
author  I  have  been  able  to  study  the  details  of  this  highly 
important  research  from  an  extra  copy  of  the  publication  in 
vol.  XII  of  the  American  Chemical  Journal  (Baltimore). 

It  is  almost  unnecessary  to  add  that  this  work  of  Pro- 
fessor Mallet  is  justly  considered  equal  to  the  best  chemical 
work  done  in  this  line  of  research  during  the  last  quarter  of 
a  century.  By  fully  making  this  opinion  our  own  we  may 
be  permitted  to  take  the  results  of  this  chemical  research  as 
representing  the  best  of  this  kind  of  chemical  work  now  on 
record. 


PLATE    I. 


GolcL    G 


MALLET:     ATOMIC  WEIGHT  OF  GOLW. 

If  Mallet's  work  were  true,  all  dots  would  lie  in  a  single  horizontal  line.     See  pp.  24-28. 


Numbers  nuxrKcd.  are  Ike 
rt-in-f)     13  .  tKL45  : 


Va.tu.e  .5.       N  from.   Syntheses    °$    5'iUcr  Ni  tra.be,    ^r  ^ 

o^     ttuSm.utfv5oni.an.    ITVS  t  ttu.kio 


STAS  :     ATOMIC  WEIGHT  OF  NITROGEN*. 
If  Stsis'  work  were  true,  all  dots  would  be  grouped  close  together.     See  pp.  186-191. 


ACTUAL    ERRORS    OF   THE    MEAN".  25 


The  Seven  Means  are  all  Mean. 

Professor  Mallet  made  seven  series  of  determinations, 
according  to  as  many  different  chemical  methods  or  pro- 
cesses. 

This  is  the  common  practice  of  chemical  science  to-day, 
and  such  different  series  are  undertaken  in  the  hope  that 
thereby  the  errors  referred  to  may  balance  and  thus  disap- 
pear from  the  final  result,  at  which  the  mean  value  of  the 
means  of  each  series  is  taken. 

Exactly  why  such  seven  errors  should  balance  and  mutu- 
ally destroy  one  another  so  as  to  give  a  final  mean  without 
error,  is  not  stated. 

The  means  given  by  Professor  Mallet  for  each  of  his  seven 
series,  and  his  final  mean,  are  as  follows  (according  to 
Ostwald,  Zeitschrift,  IV,  478;  1889)  : 

Series       I,  from  gold  chloride,       .     .     ,     .     .  Mean,  196.722 

"         II,     "     gold  bromide, 196.790 

"       III,     "     potassium  gold-chloride,       .     .     .  196.775 

"       IV,     "      trimethyl  ammonium  gold  chloride,  197.225 

"         V,     "     potassium  gold  cyanide,   ....  196.825 

tf       VI,     "     same  to  hydrogen, I97-I37 

"      VII,     "     same  to  zinc, 196.897 

General  Mean, 196.80 

While  there  thus  is  a  range  of  almost  half  a  unit  between 
the  lowest  mean  196.775  (III  Series)  and  the  highest  mean 
197.225  (IV  Series),  the  results  of  each  series  and  of  each 
individual  determination  are  given  to  the  third  decimal. 
It  would  not  look  like  exact  science  if  less  than  three  deci- 
mals were  used. 

As  the  most  probable  mean  of  the  means  of  the  seven 
series,  Professor  Mallet  gives  196.80  as  the  atomic  weight  of 
gold  according  to  his  great  chemical  research  which  has 
been  very  highly  honored. 

But  we  really  do  not  care  for  the  most  probable  mean 
value  at  all.  What  we  would  like  to  know  is  the  true  atomic 
weight  of  gold.  If  there  is  exact  science,  it  ought  to  be  able 
to  give  us  exactly  that  answer  in  one  exact  number. 


26  THE   ERRORS    OF   PRECISION. 


Our  Little  Diagram  Shows  the  Facts. 

But  the  range  of  the  individual  determinations  in  the 
seven  series  necessarily  show  still  greater  divergencies  than 
the  mean  values  of  these  series.  In  order  to  present  these 
variations  to  the  eye  as  they  really  are  so  as  to  obtain  a 
proper  conception  of  the  magnitude  of  these  variations,  I 
here  reprint  the  diagram  from  page  193  of  my  True  Atomic 
Weights  published  in  1894.  See  Plate  I. 

In  this  diagram  the  actual  values  given  by  Professor  Mal- 
let himself  are  entered  as  dots  representing  also  the  amount 
of  gold  used  in  the  particular  determination. 

The  scale  is  marked  on  the  horizontal  line  for  the  gold 
used  (in  grammes),  and  on  the  vertical  line  for  the  atomic 
-weight  found.  The  dots  representing  the  actual  determina- 
tions of  any  one  series  are  marked  in  the  same  manner,  and 
connected  by  a  line. 

The  mean  value  of  each  series  is  also  entered  by  a  dot 
surrounded  by  a  circle,  and  marked  by  the  roman  numeral 
of  that  series.  In  this  way  the  diagram  here  given  repre- 
sents graphically  and  according  to  scale  all  the  most  essen- 
tial results  of  the  chemical  work  of  Professor  Mallet,  as 
given  by  himself. 

It  is  seen,  that  neither  the  individual  determinations,  nor 
the  mean  values  of  the  series,  show  any  tendency  to  cluster 
near  any  particular  point. 

Mallet  did  not  Hit  the  Mark. 

If  the  field  represented  in  our  diagram  were  considered 
as  a  target  and  Professor  Mallet  were  to  use  seven  different 
rifles  to  hit  a  definite  point  on  that  target,  and  the  marks 
made  in  the  target  were  connected  by  lines  for  each  rifle,  we 
would  in  that  diagram  see  the  evidence  that  the  seven  rifles 
were  equally  bad,  and  the  shooting  so  scattering  as  to  show 
no  center  hit  indicated  or  marked  by  any  grouping  of  dots. 

In  fact,  the  determinations  made  by  Mallet  scatter  greatly 
and  cover  the  entire  field  on  either  side  of  197  quite  evenly, 
extending  fully  three  tenths  below  and  as  much  above  this 
line. 


ACTUAL  ERRORS  OF  THE  MEAX.  27 

If  we  don't  know  the  Tenth,  we  don't  know  the  Thousandth. 

That  is,  as  a  matter  of  fact,  the  atomic  weight  of  gold 
found  by  the  chemical  determinations  of  Mallet  ranges 
about  equally  on  both  sides  of  197  to  the  extent  of  three 
tenths,  making  the  entire  range  or  uncertainty  fully  six 
tenths.  Now  when  the  best  chemical  research  made  leaves 
the  atomic  weight  of  gold  uncertain  to  the  extent  of  the 
range  of  six  tenths  of  the  unit  employed,  we  are  justified  in 
considering  the  hundreds  and  the  thousandths  displayed  in 
this  research  as  quantities  utterly  unknown,  so  far  as  actual 
chemical  determination  is  concerned. 

Surely,  the  second  and  even  more  so,  the  third  decimal 
in  all  of  these  determinations  of  Professor  Mallet  cannot 
for  a  moment  be  taken  as  chemical  facts  determined  by 
chemical  laboratory  work,  but  they  are  evidently  not  exper- 
imental scientific  data  at  all. 

They  are  extra-polations  made  by  carrying  arithmetical 
calculations  beyond  the  reach  of  the  degree  of  accuracy  of 
the  experimental  work  done. 

Mallet  Suffers  from  Morbus  Stasii. 

Furthermore,  this  diagram,  representing  to  scale  the 
actual  values  given  by  Professor  Mallet  himself  in  the  Amer- 
ican Chemical  Journal,  shows  plainly  that  the  atomic  weight 
found  varied  considerably  with  the  amount  of  gold  actually 
used  in  the  particular  chemical  determination. 

In  Series  IV,  VII  and  III,  the  individual  dots  form  ap- 
proximately a  line  rising  as  the  amount  of  gold  increases; 
in  Series  VI  the  rise  is  seen  to  be  perpendicular.  In  Series 
I  the  values  tend  downward  as  the  amount  of  gold  in-creases. 

But  it  is  the  first  condition  of  value  of  any  series  of  chem- 
ical analysis  of  any  one  given  substance,  that  the  final 
result  must  be  independent  of  the  amount  of  material  used 
in  the  analysis. 

That  is,  the  per  cent  found  must  be  the  same,  whether  2 
or  4  or  more  grammes  of  the  material  analyzed  has  been 
employed.  Of  course,  no  two  analysis  will  give  the  same 


28  THE    ERRORS    OF    PRECISION. 

number  exactly;  but  the  variations  must  lie  on  either  side  of 
a  horizontal  line  in  a  diagram  of  the  kind  here  used. 

If  a  chemist  engaged  by  a  firm  to  analyze  a  limestone 
should  hand  in  a  report  showing  clearly  that  by  his  method 
of  analysis  he  had  found  the  percentage  of  lime  to  run  up 
(or  down)  with  the  amount  of  limestone  operated  upon  by 
him,  the  firm  would  most  likely  not  entrust  any  further  work 
to  this  chemist. 

We  regret  to  find  by  these  symptoms,  that  Professor 
Mallet  has  suffered  from  Morbus  Stasii  for  many  years. 
This  should  be  remembered  before  judging  his  work  harshly. 

This  is  so  much  the  more  called  for  as  we  notice  his  case 
complicated  by  the  incipient  stages  of  Furor  Clarkii. 

Our  Conclusion. 

Therefore,  the  only  legitimate  conclusion  that  can  be 
drawn  from  the  results  given  by  Professor  Mallet  and  repre- 
sented graphically  to  scale  in  our  diagram,  is  that  the 
methods  used  are  not  chemically  satisfactory,  because  they 
give  results  showing  the  existence  of  errors  varying  with 
the  amount  of  matter  operated  upon. 

Instead  of  taking  the  mean  of  eaCh  series  as  the  true 
value,  the  entire  work  should  be  discarded  as  tmreliable. 

We  have  purposely  dwelt  upon  these  details  of  the  noted 
determinations  of  the  atomic  weight  of  gold  by  Professor 
Mallet  because  the  recognized  high  value  of  the  chemical 
work  shows  strikingly  the  necessity  of  some  critical  exami- 
nations of  such  work  by  methods  not  yet  used  in  the 
chemical  laboratory,  but  which  can  be  drawn  from  the 
general  science  of  quantity  and  form,  that  is,  from  mathe- 
matics and  common  sense. 

VI.     ERRORS  IN  PRECISION. 

Incredible  as  it  may  seem  to  any  one  not  familiar  with 
the  causes  that  have  led  to  the  existing  practice  of  calcula- 
tion among  chemists  engaged  in  the  determination  of  the 
atomic  weights  of  the  elements,  we  find,  as  a  matter  of  fact, 
that  two  errors  of  method  are  quite  generally  committed, 
either  one  of  which  would  suffice  to  vitiate  the  results  pro- 


ERRORS    IX    PRECISION*.  29 

claimed   as  the  atomic  weight   determined  often   by   great 
skill  and  patience  in  the  chemical  laboratory. 

The  Two  Fatal  Common  Errors. 

First,  the  chemist  will  calculate  the  atomic  weight  with 
two  or  even  more  decimals,  when  a  simple  examination 
would  have  convinced  him  that  these  decimals  have  abso- 
lutely no  value  whatever,  being  far  beyond  the  limit  of 
precision  of  his  chemical  work. 

Second,  the  chemist  will  start  in  this  calculation  with 
the  data  of  one  of  the  national  leaders  of  organizations,  and 
if  these  data  are  wrong  (as  we  shall  find  them  to  be)  he  will 
necessarily  get  erroneous  values  from  the  very  best  laboratory 
work  he  can  produce. 

It  is  very  unpleasant  to  make  such  sweeping  statements; 
but  it  is  not  our  fault  that  these  statements  are  an  exact  rep- 
resentation of  the  actual  facts. 

And  if  the  reader  for  a  moment  will  free  his  miud  from 
the  power  of  authority  whether  it  be  of  numbers,  name  or 
station,  he  will  see  the  necessity  of  the  full  recognition  of 
this  state  of  facts  in  order  to  clear  the  way  to  obtain  true 
results  from  good  chemical  work. 

Don't  give  us  your  Fancy  for  Fact. 

First,  we  must  demand  that  no  chemist  publish  to  the 
world  an  atomic  weight  as  representing  his  laboratory  work, 
his  chemical  research  of  precision,  when,  as  a  matter  of  fact, 
he  gives  decimals  that  have  no  foundation  whatever  in  his 
chemical  determination  and  weighings,  but  simply  are 
products  of  his  own  imagination. 

That  which  is  common  practice  in  the  Laboratory  of 
Moissan  of  Paris,  presented  by  him  to  the  Academy  of 
Sciences  of  Paris,  and  recommended  by  the  present  Section 
of  Chemistry  of  that  Academy  for  the  Prize  Vaillant  which 
was  granted  by  the  Academy  in  December  last,  cannot  be  a 
special  sin  when  committed  in  an  American  Laboratory  and 
published  in  our  Journals  of  Chemistry.  I  refer  to  the  work 
of  Henry  Gautier  on  boron,  in  the  Laboratory  of  Moissan. 


30  THE    ERRORS    OF    PRECISION. 

To  state  as  experimentally  established,  as  data  of  labor- 
atory work,  numbers  and  decimals  that  are  merely  and 
absolutely  fancy,  is  about  as  disgusting  and  reprehensible  an 
act  as  can  be  committed  against  the  true  progress  of  science. 


Edgar  F.  Smith  and  W.  L.  Hardin. 

Still  I  shall  here  take  the  special  example  for  illustration 
from  the  laboratory  of  Edgar  F.  Smith  of  the  University  of 
Pennsylvania,  because  it  was  published  in  the  Thesis  of 
Willet  Lepley  Hardin  in  1896,  and  in  various  Journals,  after 
the  error  had  been  fully  shown  by  me  in  letters  to  Professor 
Smith  in  May,  1895. 

We  take  then,  as  special  case  for  the  study  of  the  first 
great  common  error  in  calculation  of  atomic  weight  deter- 
minations, the  six  electrolyses  of  mercuric  oxide  made  by 
W.  L.  Hardin  in  the  laboratory  of  Edgar  F.  Smith. 

The  mercuric  oxide  taken  and  the  mercury  obtained  are 
the  weighed  quantities.  The  weighings  are  given  to  the 
hundredth  of  a  milligramme  (by  oscillation  method). 

Accordingly,  the  hundredth  of  the  milligramme  being 
the  last  figure  determined,  is  simply  the  nearest  full  number 
of  that  place,  and  subject  to  the  usual  limitation  of  a 
possible  error  of  at  most  half  a  unit.  In  other  words,  the 
utmost  that  can  be  claimed  is  that  the  weighings  given  are 
subject  to  an  uncertainty  of  half  a  hundredth  of  a  milli- 
gramme, or  half  a  unit  in  the  fifth  place  of  the  gramme. 

For  each  of  his  six  determinations  Mr.  Hardin  calculates 
the  corresponding  atomic  weight,  and  gives  the  results  with 
two  decimals  (Thesis,  p.  23).  The  weighings  and  the  cal- 
culated atomic  weights  are  identically  the  same  communi- 
cated to  me  in  May,  1895,  by  the  courtesy  of  Prof.  Smith. 

But  the  weighings  do  not  sustain  any  such  atomic  weights, 
and  the  publication  of  these  atomic  weights  as  experimental 
data  is  false  in  fact  and  fraudulent  in  nature. 

Taking  Hg  at  200,  the  oxide  exceeds  the  metal  by  exactly 
S  per  cent.  Taking  the  mercury  as  reported  by  Hardin,  and 
adding  8  per  cent  thereto,  we  obtain  exactly  the  weight  of 


KRRORS    IX    PRECISION".  3! 

the   mercuric   oxide   as    determined    by    him    to    the    exact 
hundredth  of  a  milligramme. 

This  is  as  perfectly  and  absolutely  the  case  that  this  series 
of  determinations,  if  true,  is  most  marvelous  and  created  a 
suspicion  of  being  manufactured. 

In  the  reduction  by  Mr.  Hardin  the  atomic  weight  of 
mercury  is  affected  with  from  o  to  6  hundredths  above  200. 
These  atomic  weights  are  published  as  the  expression  of  the 
weighings,  and  are  so  taken  by  the  chemical  public. 

Such  data  as  these  are  not  data  of  observation,  for  they 
are  not  representing  the  stated  weighings;  they  represent 
imagination  and  not  observed  facts. 

It  is  true,  Mr.  Hardin  has  said  this  series  is  vitiated  by 
other  experiments  made  with  larger  amounts;  but  these  six 
determinations  still  stand  on  record  as  data  of  actual  experi- 
mental determination. 

If  we  are  to  have  true  atomic  weights,  we  must  first  blot 
out  all  false  statements  of  fact,  all  invented  atomic  weights, 
from  the  records  and  publications. 

It  is  well  known,  that  such  calculation  of  decimals  can 
not  be  carried  beyond  the  limit  of  precision.  Every  manual 
on  experimentation  gives  rules  for  such  limitation,  as  may 
be  seen  in  Kohlrausch. 

v  My  method  is  perhaps  the  simplest,  equally  applicable  in 
all  cases,     ftls  found  in  my  Elements  of  Physics,  p.  12  ;  1870. 

It  consists  in  actually  calculating  the  value  sought  from 
the  formula  by  using  the  actual  data  determined  and  also 
modified  by  one  unit  in  the  last  place.  The  difference 
between  the  two  values  evidently  is  the  variation  for  that 
unit. 

In  the  case  before  us,  we  must  bear  in  mind,  that  for  a 
given  amount  of  oxide,  the  increase  in  mercury  would 
necessitate  a  decrease  in  oxygen  given  by  difference. 

Accordingly,  for  the  first  determination,  in  which  262.23 
milligrammes  of  the  oxide  gave  242.81  mgr.  mercury — and 
by  difference  19.42  mgr.  oxygen,  we  calculate  Hg  both  for 
these  weights  and  for  242. 82  and  19.41.  We  find  a  change  in 
Hg  of  o.i i. 

Accordingly,  as  lialf  a.  hundredth  of  a  milligramme  is  the 


32  THE    ERRORS    OF    PRECISION. 

uncertainty  of  weighing  the  corresponding  uncertainty  in 
the  atomic  weight  is  0.055  or  practically  0.06  units  in  Hg. 

But  the  greatest  decimal  given  by  Hardin  is  precisely 
0.06.  The  determinations  of  Hardin  are  uncertain  to  this 
extent.  Hence  these  fractions  of  Hardin  are  not  experi- 
mentally determined.  They  represent  nothing  but  his  own 
imagination. 

For  the  fifth  determination  the  change  per  unit  (in  hun- 
dredth mgr.)  amounts  to  o.io;  hence  the  uncertainty  in  the 
value  of  Hg  is  0.05.  The  fraction  0.03  of  Hardin  is  within 
this  limit  of  uncertainty.  His  statement  Hg  =  200.03  *s  n°t 
a  statement  of  fact,  is  not  warranted  by  his  weighings.  He 
is  drawing  on  his  own  imagination. 

For  the  fourth  determination,  in  which  the  weight  of 
the  oxide  taken  is  stated  to  be  141.48  mgr.  the  change  (per 
unit  in  hundredth  milligramme)  is  0.20;  hence  the  uncer- 
tainty in  the  atomic  weight  Hg  amounts  to  o.io. 

Now  in  this  instance,  Mr.  Hardin  gives  Hg  =  200.00;  both 
of  these  decimals  are  due  to  his  own  imagination,  since  his 
weighings  leave  the  atomic  weight  uncertain  to  the  unit  in 
the  first  place. 

In  other  words,  in  the  stated  value  Hg  =  200.00  Mr. 
Hardin  assumes  for  his  determinations  an  accuracy  one 
hundred  times  the  actual  precision  of  his  own  weighings! 

Such  statements,  pretending  to  be  statements  of  experi- 
mental facts,  are  a  blot  upon  science  and  block  the  way  of 
the  truth;  for  they  are  false  in  fact,  merely  imagination  and 
fancy.  They  are  essentially  fraudulent,  for  they  do  not 
present  fact  as  they  pretend  to  do. 

VII.     ERRORS  DUE  TO  FALSE  DATA. 

The  second  mathematical  error  universally  committed  by 
the  chemists  of  the  present  is  in  itself  fatal  to  the  produc- 
tion of  a  true  value  of  the  atomic  weight  or  even  a  correct 
expression  of  the  often  admirable  chemical  laboratory  work 
done. 

We  refer  to  the  common  habit  of  "adopting"  some  set 
of  values  of  atomic  weights  in  the  calculation  required, 


ERRORS    DUE   TO    FALSE   DATA.  33 

without  making  sure  that  these  auxiliary  atomic  weights  are 
themselves  correct. 

It  is  incredible,  but  true,  that  chemists  will  reduce  their 
often  excellent  laboratory  work  by  means  of  auxiliary  atomic 
weights  furnished  by  committees  of  chemical  societies  or 
some  official  chemist  without  allowing  for  the  possible  errors 
of  these  auxiliary  data. 

Necessarily,  the  errors  of  these  data  of  the  auxiliary 
atomic  weights  adopted,  will  affect  the  results  calculated 
from  the  new  chemical  determinations. 

Ramsay  and  Aston. 

The  opening  words  of  the  otherwise  admirable  paper  of 
Ramsay  and  Aston  on  the  atomic  weight  of  boron  are : 

"  The  atomic  weights  employed  in  this  paper  are  those 
"given  by  Clarke:  Ag  =  107.92,  Na  =  23.05,  01  =  35.45, 
"  Br  =  79.95,  H  =  i. 008  and  O  =  16."  See  Journal  Chemical 
Society,  vol.  63,  p.  215;  London,  1893. 

If  now  each  and  every  one  of  these  five  values  in  reference 
to  the  oxygen  standard  be  affected  by  errors,  these  errors 
will  necessarily  affect  all  the  calculated  values  of  Ramsay 
and  Aston. 

Let  us  suppose  for  a  moment,  that  these  excellent  chem- 
ists had  completed  all  their  chemical  work  with  absolute 
precision  and  therefore  free  from  experimental  error,  the 
results  published  would  still  be  erroneous  to  the  extent  of 
the  effect  of  the  errors  of  these  five  atomic  weights  of  Clarke 
"  employed  "  by  them. 

We  shall,  in  another  section,  show  conclusively  that  these 
chemists  thus  falsified  their  own  most  excellent  laboratory 
work. 

We  may  already  at  this  point  call  attention  to  the  fact 
that  these  authors  find  the  atomic  weight  of  boron  10.965  by 
calculating  from  sodium  chloride,  while  calculating  from 
silver  chloride  they  find  it  11.084.  See  determinations  Nos. 
22  to  26. 

As  the  atomic  weight  of  chlorine  appears  in  both  of  these 
compounds,  the  very  large  discrepancy  of  0.119  is  connected 


34  THE    ERRORS    OF    PRECISION. 

with  the  Clarkian  atomic  weights  for  Xa  and  Ag  "  em- 
ployed." This  amounts  to  one  per  cent  on  the  atomic 
weight — an  enormous  error! 

It  is  passing  strange  that  good  chemists  continue  to 
reduce  their  weighings  by  such  data  and  coolly  recognize 
the  discrepancy  of  more  than  one-tenth  in  final  means 
though  they  have  been  giving  single  determinations  to  the 
thousandth. 

Have  such  chemists  never  felt  the  necessity  of  inquiring 
into  the  cause  of  such  discrepancies,  exceeding  hundredfold 
the  supposed  accuracy  of  their  own  chemical  work? 

H.  Moissan  and  H.  Gautier. 

The  atomic  weight  of  boron  has  also  more  recently  been 
determined  in  the  laboratory  of  the  University  of  Paris, 
under  the  direction  of  Moissan,  by  Henri  Gautier,  which 
determination  has  been  greatly  honored  by  the  Academy 
of  Sciences  of  Paris,  granting  the  Vaillant  Prize  to  the 
young  chemist  upon  the  recommendation  of  the  entire 
section  of  chemistry,  for  which  section  Moissan  was  the 
spokesman  (rapporteur). 

In  the  reduction  of  his  often  admirable  laboratory  work, 
Henry  Gautier  uses  "the  table  of  atomic  weights  published 
in  1898  by  Landolt,  Ostwald  and  Seubert"  throughout  his 
reductions. 

Consequently,  he  will  have  all  his  chemical  determina- 
tions infected  by  the  errors  of  these  atomic  weights  of  the 
German  Chemical  Society. 

Under  Moissan,  good  French  laboratory  work  is  spoilt  or 
falsified,  by  reducing  it  by  German  atomic  weights. 

That  such  is  the  case  I  have  shown  in  my  two  articles 
communicated  to  the  Academy  in  the  sessions  of  June  18 
and  July  2,  1900,  which  were  published  in  full  in  the  Comptes 
Rendus. 

That  a  great  Academy  of  Science  grants  a  valuable  prize 
for  work  which  has  been  shown  in  its  own  publications  to 
give  false  values  is  a  rather  important  fact  to  take  note  of. 

When  we  come  to  the  study  of  the    atomic   weight   of 


ERRORS    DUE   TO    FALSE    DATA.  35 

boron  we  shall  give  ample   data   on   these    astounding  and 
most  characteristic  points. 

There  is  not  a  shadow  of  doubt  but  the  values  crowned 
by  the  Academy  of  Sciences  of  Paris  are  not  true  to  nature, 
and  this  fact  was  fully  established  by  my  papers  printed  in 
the  Comptes  Rendus  of  that  academy  six  months  before 
conferring  that  prize. 

Armand  Gautier  and  J.  Aloy. 

To  what  extent  such  erroneous  data  (auxiliary  atomic 
weights)  will  falsify  the  results  of  the  chemical  work,  we 
will  show  by  one  single  example. 

This  case  we  shall  also  take  from  one  of  the  highest 
sources  of  chemical  science,  from  the  noted  laboratory  of 
Professor  Armand  Gautier,  of  the  University  of  Paris,  where 
Mr.  J.  Aloy  has  made  the  research,  the  results  of  which 
Professor  Armand  Gautier  himself  presented  to  the  Acade- 
my of  Science  on  March  4,  1901  (C.  R.  132,  p.  551-553). 

In  this  research  the  atomic  weight  of  Uranium  is  deter- 
mined by  a  process  of  ignition  and  combustion,  the  nitrate 
giving  free  nitrogen  gas  and  uranic  oxide.  The  nitrogen  is 
measured,  the  oxide  is  weighed. 

No  data  of  weights  are  given.  The  volume  of  nitrogen, 
and  the  atomic  weight  of  Uranium  resulting  are  stated. 

This  is  a  very  improper  way;  the  direct  data  of  the 
quantities  determined  must  be  given  to  admit  the  research 
to  the  records  for  any  use  whatsoever. 

No  critical  examination  is  possible  in  the  absence  of  the 
statement  of  the  real  weights  determined.  Moissan,  in  his 
determinations  of  the  atomic  weight  of  fluorine  has  also 
omitted  these  essential  data;  hence  his  determinations  could 
not  be  introduced  into  the  general  record.  See  True  Atomic 
Weights,  1894,  p.  195. 

It  is  to  be  hoped  that  this  singular  practice  of  Moissan 
and  Gautier,  will  not  become  general  in  France.  It  would 
certainly  blot  out  French  work  from  the  record. 

In  the  absence  of  the  necessary  weights  of  the  two 
quantities  determined  in  each  experiment,  we  are  compelled 
to  test  the  results  given  by  an  inverse  process. 


36  THE    ERRORS    OF    PRECISION*. 


The  atomic  weight  in  reference  to  nitrogen  is  given,  and 
this  atomic  weight  of  nitrogen  "is  taken  at  14.04." 

The  atomic  weight  of  uranium  stated  ranges  from  239 .3 
to  239.6  occuring  each  once.  Two  determinations  gave 
239.5  and  four  gave  239-4-  Eight  determinations  were  made. 

Accordingly,  the  analytical  ratio  Ur  :  N  ranged  17.044 
to  17.066. 

But  if  instead  of  taking  the  atomic  weight  of  nitrogen  as 
14.04  it  were  taken  at  14  exactly,  the  above  ratios  multiplied 
by  14  would  give  for  uranium  values  ranging  from  238.6  to 
238.9,  which  are  0.7  lower  than  the  values  reported  by 
A.  Gautier  on  the  assumption  that  N  is  14.04. 

Here  we  have  a  change  of  seven  tenths  of  a  unit  in  the 
atomic  weight  of  uranium  consequent  upon  the  slight 
change  of  the  atomic  weight  of  nitrogen  from  14.04  to  14, 
amounting  to  four  hundreths  only. 

All  previous  determinations  make  it  highly  probable  that 
Ur  is  240.  Gautier  reports  239.4  for  N  =  14.04;  for  N  =  14 
it  would  come  down  to  238  .7. 

This  shows  strikingly  the  great  importance  of  the  values 
of  the  auxiliary  atomic  weights  used  in  the  calculations 
of  the  chemical  experiments  made,  that  is,  in  the  so-called 
reduction  of  the  work. 

The  very  considerable  change  or  uncertainty  also  empha- 
sizes the  necessity  of  giving  the  original  data  of  the  deter- 
minations, the  direct  weighings  (reduced  to  vacuum  only), 
so  that  the  chemical  work  done  may  be  used  and  not  have 
to  be  thrown  away. 

We  shall  find,  in  a  subsequent  part  of  this  work,  that  the 
real  atomic  weight  of  nitrogen  is  14  exactly  and  not  14.04. 
The  weighings  of  Lord  Rayleigh  have  made  the  Stasian 
value  14.04  absolutely  impossible.  See  my  General  Chem- 
istry, 1897,  p.  378. 

Since  now  the  atomic  weight  of  uranium  will  be  found  to 
be  truly  240,  according  to  unquestionable  methods  of  work, 
the  new  determinations  made  in  this  Laboratory  of  Armand 
Gautier  have  only  added  another  false  value  to  the  chemical 
record. 

In  fact,  the  work  done  by  Mr.  J.  Aloy  in  the  laboratory 


ERRORS    DUE   TO   FALSE   DATA.  37 

of  A.  Gautier,  has  been  absolutely  thrown  away,  as  utterly 
worthless. 

My  Method  in  the  Comptes  Rendus. 

The  necessity  of  fixed  and  true  values  of  the  auxiliary 
atomic  weights  is  so  palpable  that  it  should  never  have  been 
overlooked. 

That  the  use  of  different  values  of  such  auxiliary  atomic 
weights  in  different  hands  must  give  different  results  for  the 
same  atomic  weight,  even  if  the  chemical  determinations 
were  exactly  the  same,  should  never  have  been  lost  sight  of. 

Mv  general  method  of  keeping  an  exact  account  of  the 
effect  of  any  slight  change  in  the  atomic  weights,  was  pub- 
lished in  the  Comptes  Rendus  for  1893  (T.  116,  p.  695-698; 
March,  1893). 

It  is  deplorable  that  the  famous  directors  of  the  great 
laboratories  supported  by  the  French  Nation  are  unable  to 
profit  by  the  contents  of  the  Comptes  Rendus  of  the  Acad- 
emy of  Sciences  of  Paris. 

It  seems  strange  that  these  most  eminent  Chemists  of 
Paris  do  not  prevent  the  falsification  of  excellent  chemical 
determinations  of  their  French  students  by  the  use  of  incor- 
rect German  atomic  weights. 

But  if  these  most  eminent  Chemists  of  Paris  persist  in 
disregarding  the  most  obvious  and  elementary  principles  of 
mathematics,  the  work  of  their  students  will  necessarily  be 
in  error,  and  worthless  to  Science. 

We  shall  see  whether  modern  chemistry  will  accept  the 
conferring  of  a  prize  by  the  Academy  of  Sciences  of  Paris, 
at  the  recommendation  of  its  section  of  chemistry,  sufficient 
to  adopt  these  palpably  false  values  of  the  atomic  weight  of 
boron  as  true. 

I  may  be  pardoned  the  expression  of  the  hope,  that  the 
great  laboratories  of  Paris  will  in  a  near  future  pay  some 
attention  to  these  methods  of  reduction. 

It  is  but  a  few  years  since  Schutzenberger  and  Friedel 
have  been  lost  to  French  Chemistry.  It  is  particularly 
regretted  that  A.  Gautier  has  so  soon  forgotten  his  col- 


38  THE    ERRORS    OF    PRECISION. 

leagues,  who  in  publications  and  in  their  rostrum  made 
practical  use  of  my  work. 

It  is  not  for  me  to  examine  how  it  happens  that  these 
leading  chemists  of  France  are  foisting  upon  the  chemical 
public  of  the  world,  work  crowned  at  their  recommendation 
by  the  famous  Academy  of  Sciences  of  Paris,  work  that  gives 
new  data  notoriously  and  necessarily  erroneous,  because 
these  great  chemists  have  not  found  time  to  intelligently 
read  the  papers  published  in  the  Comptes  Rendus  of  their 
own  academy. 

So  far  as  Professor  A.  Gautier  is  concerned,  he  has 
repeatedly  acknowledged  the  value  of  my  contributions  to 
the  Comptes  Rendus  and  the  importance  of  my  critical 
examination  of  the  work  of  Stas,  which  implies  the  falsity 
of  the  value  of  14.04  for  nitrogen. 

Is  this  throwing  away  the  labor  of  young  French  Chem- 
ists and  the  production  of  new  errors  and  false  atomic 
weights  in  any  way  connected  with  that  old  French  Institu- 
tion: Le  Cumul? 

VIII.     ERRORS  OF  WEIGHING. 

The  last  laboratory  operation  in  a  chemical  determina- 
tion of  the  atomic  weight  is  the  -weighing  of  the  product 
obtained. 

The  first  operation,  after  obtaining  the  pure  material  or 
substance  was  likewise  a  weighing,  namely  the  determination 
of  the  exact  amount  of  substance  operated  upon. 

These  weighings  may  be  reduced  to  vacuum. 

The  weight  s  of  the  substance  taken,  and  the  weight/  of 
the  final  product  obtained,  are  the  only  data  of  the  actual 
experimental  determination  made. 

To  express  these  results  in  a  common  unit,  all  experi- 
ments are  referred  to  the  unit  of  weight,  by  dividing  the 
weight  of  the  product  by  that  of  the  substance  used. 

The  quotient  thus  obtained  is  the  only  true  final  expres- 
sion of  the  experiment  or  determination  made.  We  call 
this  quantity  the  analytical  ratio. 

Every  individual   determination    actually   made   is   thus 


ERRORS    OF   WEIGHING. 


39 


expressed  by  one  single  number,  this  analytical  ratio,  a, 
which  is  the  amount  of  product  obtained  for  the  unit  of 
•weight  of  substance. 

This  ratio  is,  as  stated  above  in  words :     a  =  -H-  . 

In  order  that  there  may  be  no  misunderstanding  about 
this  most  important  —  though  really  very  simple  —  matter, 
we  will  take  from  the  record  one  of  the  most  noted  cases, 
namely  the  five  combustions  of  diamond  in  oxygen  by 
Dumas  in  1840. 

We  copy  the  data  from  the  original  publication,  Annales 
de  Chimie  et  de  Physique,  3rd  series,  Tome  I,  for  January, 
1841.  It  is  reprinted  in  the  "  Oeuvres"  of  Stas,  vol.  I,  pp. 
235-287 ;  Brussels,  1894.  See  also  our  True  Atomic  Weights, 
pp.  20-22,  1894. 

Dumas.    Combustion  of  the  Diamond. 


Diamond. 

Pure 

Carbon 

Analytical 

Exp. 

Number. 

Weight. 

Ashes. 

Carbon. 

Dioxide. 

Ratio. 

I 

Scales 

717 

9 

708 

2598 

3-6695 

2 

18 

865 

i 

864 

3167.5 

3.6661 

3 

6 

1221 

2 

1219 

4465 

3.6628 

4 

5 

1233 

I 

1232 

4517 

3-6664 

5 

Grains 

1377 

2 

1375 

5041 

3.6662 

All  -weights  in 

Milligra  m  m  es  . 

Mean 

3-6663 

This  is  all  we  learn  from  the  five  famous  combustions  of 
diamond  made  by  Dumas  in  1840,  and  in  which  Stas  was 
privileged  to  assist. 

The  five  combustions  are  each  represented  by  the  final 
analytical  ratios  (product  obtained  divided  by  substance 
used). 

These  ratios  represent  the  weight  of  carbon  dioxide 
obtained  by  the  combustion  of  a  unit  of  weight  of  the  pure 
carbon  of  the  diamond. 

These  five  ratios  agree  so  closely  that  we  are  authorized 
to  calculate  the  mean  value  of  all. 

But  we  must  not  conclude  that  this  mean  value  3.66  63 
more  nearly  represents  the  true  value  than  either  one  of 
these  individual  ratios. 


THE    ERRORS    OF    PRECISION. 


We  have  sufficiently  explained  this  point  and  shall  have 
to  come  back  to  it  when  we  reach  the  discussion  of  the 
atomic  weight  of  carbon  in  relation  to  that  of  oxygen. 

Precision  of  Weighing. 

At  this  point  we  shall  now  consider  the  accuracy  of 
weighing  and  the  degree  of  certainty  of  the  ratios  calculated, 
that  is,  the  number  of  decimals  that  are  reliable. 

First,  as  to  the  accuracy  of  weighing,  we  know  that  it 
generally  exceeds  the  accuracy  of  the  chemical  operations 
and  processes  involved  in  changing  the  substance  taken  into 
the  final  product. 

It  is  therefore,  on  the  whole,  to  be  carefully  born  in 
mind,  that  the  accuracy  of  weighing  exceeding  that  of  the 
chemical  processes,  the  accuracy  of  the  final  weights  is  less 
than  the  accuracy  of  the  actual  weighings,  and  especially 
that  the  ratio  calculated  is  subject  to  even  an  uncertainty  due 
to  the  most  accurate  part  of  this  work,  namely,  the  weighing. 

It  is  of  the  highest  importance  that  this  subject  should 
be  fully  understood  in  order  that  the  data  of  experience 
obtained  in  the  chemical  laboratory  can  be  taken  for  what 
they  really  are  —  neither  less  nor  more  accurate  than  the 
actual  work  done. 

We  therefore  shall  consider  the  points  mentioned  sepa- 
rately, one  at  a  time,  with  such  detail  as  seems  necessary. 

The  Balance  used  by  Dumas. 

The  weighings  above  given  are  expressed  in  milli- 
grammes; only  in  one  single  instance  is  the  half  milligramme 
stated.  This  does  not  mean  that  this  half  milligramme  was 
actually  weighted  by  a  weight,  but  7  milligrammes  were 
plainly  insufficient  and  8  milligrammes  as  much  in  excess. 

This  little  circumstance  of  the  single  half-milligramme 
recorded  shows  that  the  weighings  were  exact  to  the  nearest 
milligramme,  and  no  more. 

Dumas  himself  states  that  the  ie  balance  used  very  readily 
shows  the  milligramme"  (Oeuvres,  p.  251).  He  mentions 


ERRORS    OF   WEIGHING.  4! 

this  fact  incidentally,  when  stating  that  the  diamond  burnt 
surely  did  not  contain  hydrogen — not  enough  to  give  one 
single  milligramme  of  water  from  the  combustion  of  a 
diamond  weighing  1,500  milligrammes. 

As  will  readily  be  understood,  this  shows  that  a  diamond 
of  13,500  milligrammes  cannot  contain  as  much  as  one 
milligramme  of  hydrogen. 

Considered  with  reference  to  the  analytical  balances  now 
in  the  laboratories,  the  balance  used  by  Dumas  in  this  great 
research  was  but  an  inferior  instrument. 

This  shows  once  again,  that  the  accuracy  of  the  instru- 
ment at  hand  counts  for  very  little  in  the  value  of  real 
scientific  work  done. 

Indeed  I  am  tempted  to  say,  that  the  very  fine  balances 
now  in  our  laboratories,  are  one  cause  of  the  inferior  work 
done  in  these  laboratories  the  last  forty  years. 

The  Balance  used  by  Berzelius. 

If  now  we  turn  further  back  in  the  history  of  this  great 
determination  of  the  atomic  weights  of  the  elements  to  the 
real  founder  of  this  work,  Berzelius,  we  find  that  the  balance 
used  by  him  during  the  first  twenty  years  was  much  inferior 
to  the  balance  of  Dumas  of  1840. 

For  we  find,  in  the  earliest  data  of  Berzelius  for  lead,  that 
he  ordinarily  took  ten  grammes  of  lead  and  gave  the  weight 
of  the  product  to  the  centigramme  only. 

Quite  a  number  of  the  actual  weighings  of  Berzelius  are 
given  on  pages  13  and  15  of  our  True  Atomic  Weights, 
1894.  He  gives  generally  the  centigramme  only;  at  times 
he  states  the  half  centigramme  by  entering  5  as  third  decimal. 

We  are  therefore  certain,  that  Berzelius,  about  1810, 
weighed  habitually  to  the  centigramme  only,  while  Dumas 
at  1840  weighed  to  the  milligramme. 

Our  Fine  Balances. 

As  a  matter  of  fact,  the  best  work  done  to-day  in  our 
chemical  laboratories  is  not  reliable  below  the  tenth  of  a 
milligramme. 


THE    ERRORS    OF    PRECISION. 


But  the  fine  analytical  balances  in  actual  use  in  our  labor- 
atories permit,  by  the  so-called  method  of  oscillations,  to 
calculate  the  weight  to  the  hundredth  of  the  milligramme. 

Yea,  the  weighings  of  Morley  are  stated  to  the  thousandth 
of  the  milligramme,  and  those  of  Ramsay  and  Aston 
before  referred  to  are  stated  to  the  ten-thousandth  of  the 
milligramme. 

To  the  uniniated  it  may  appear  as  prima-facie  evident, 
that  the  apparent  weighings  being 

of  Berzelius  to  the  centigramme  or  2nd ; 

of  Dumas  to  the  milligramme  or  3rd ; 

of  the  present  to  the  tenth  mgr.  or  4th ; 

of  E.  F.  Smith  to  the  hundredth  mgr.  or    5th; 
of  Morley  to  the  thousandth  mgr.  or  6th ; 

of  Ramsay  to  the  ten  thousandth  mgr.  or  7th 
decimal  of  the  gramme,  the  work  of  Ramsay  was  one  hundred 
thousand  times  as  accurate  as  that  of  Berzelius. 

Let  us  see  about  the  facts ;  for  we  can  not  afford  to  take 
sham  accuracy  for  the  truth. 


Weighing  the  Weighers. 

Now  both  Berzelius,  in  1826,  and  Ramsay  and  Aston,  in 
1893,  determined  the  amount  of  water  of  crystallization  in 
borax. 

Berzelius  in  three  determinations  found  47.10  per  cent; 
that  is,  his  analytical  ratio  was  0.4710 being  the  amount  per 
unit  of  weight. 

Ramsay  and  Aston  found  a  mean  ratio  of  0.471677. 
Apparently  they  determined  this  ratio  to  the  millionth,  while 
Berzelius  reached  the  hundred  thousandth  only. 

But  when  we  examine  the  seven  individual  determina- 
tions made  by  Ramsey,  we  find  they  run  all  the  way  from 
0.471099  as  the  lowest  to  0.472026  as  the  highest.  See  1.  c., 
Journal  Chem.  Soc. 

But  the  variation  thus  actually  affects  the  third  decimal, 
which  being  uncertain,  all  the  rest  from  the  fourth  to  the 
sixth  are  —  well,  good  for  nothing  as  experimental  data. 


ERRORS    OF    WEIGHING.  43 

In  other  words,  the  chemical  work  of  Berzelius,  probably 
effected  by  means  of  a  good  centigramme  balance,  is  fully  as 
accurate,  chemically  speaking,  as  the  most  pretentious  weigh- 
ings cm  record  made  to  the  ten-millionth  of  the  gramme, 
by  Ramsay  and  Aston  in  1893,  using  one  of  the  finest 
balances  ever  made  and  supplying  the  fine  weights  by  calcu- 
lating from  the  oscillations  of  the  pointer  over  the  scale. 

We  shall  learn,  after  a  little,  that  Berzelius  really  got 
nearer  the  truth  with  his  centigramme  balance  than  did 
Ramsay  with  his  balance  one  hundred  thousand  times  more 
sensitive  (at  least  on  the  record  printed)  than  the  balance  of 
Berzelius. 

Great  Chemist,  Poor  Balance. 

If  we  were  given  to  calculating  the  "weight"  of  the 
work  done  by  chemists,  as  is  customary  at  Washington, 
what  would  be  the  comparative  value  of  these  chemists? 

The  "  weight "  of  determinations  varying  inversely  as  the 
" square"  of  the  "  errors/'  it  would  follow  that  Berzelius  was 
in  1826,  a  10,000,000,000  times  better  chemist  as  Ramsay 
in  1893. 

But  it  is  well  understood  that  we  do  not  indulge  in  such 
calculations.     They  belong  to  the  scientific  departments  at  &  (fat  &*/&>* 
Washington.    However,  this  result  remains:   Berzelius  came 
nearer  the  truth  with  his  simple  means  than  did  Ramsay 
with  all  the  refinement  of  modern  science. 

What  then  is  the  real  chemical  lesson  which  we  should 
learn  from  this  remarkable  incident  put  on  record  in  all 
works  on  atomic  weight  determinations — though,  perhaps, 
not  brought  out  quite  as  strikingly. 

The  real  errors  committed  by  Ramsay  and  Aston  in  this 
work  were : 

First,  giving  a  fictitious  degree  of  accuracy — at  least  two 
decimals  too  many. 

Second,  using  a  balance  much  too  fine  for  the  chemical 
work  to  be  done. 

Third,  they  did  not  realize  that  the  finest  weighing 
cannot  possibly  compensate  for  the  lack  of  purity  of  sub- 
stance or  the  absence  of  perfection  in  the  chemical  operation. 


44  THE   ERRORS    OF    PRECISION. 

So  long  as  it  is  impossible  to  obtain  absolutely  pure 
crystals  of  borax,  having  exactly  all  the  theoretical  water  of 
crystallization  and  no  more,  it  is  absurd  to  weigh  more 
accurately  than  to  the  milligramme. 

The  Man  and  the  Balance. 

In  concluding  this  most  instructive  episode  from  the 
history  of  atomic  weight  determinations,  I  trust  the  reader 
hereafter,  when  studying  some  new  atomic  weight  determi- 
nation and  noticing  how  the  accuracy  of  the  balance  and 
weights  used  is  extolled,  will  not  conclude  that  this  guaran- 
tees accuracy  in  the  final  results. 

If  the  man  behind  the  gun  tells  on  the  result  in  battle, 
the  chemist  before  the  balance  tells  on  the  resulting  atomic 
weight. 

What  has  been  said  may  suffice  on  the  subject  of  weigh- 
ing. A  few  words  are  still  required  on  the  calculation  of 
the  analytical  ratio,  especially  as  to  the  number  of  decimals 
that  ought  to  be  retained. 

Of  course,  according  to  the  novice  it  is  only  a  question 
of  physical  endurance  and  space  which  limits  the  number 
of  decimals  in  the  quotient  calculated  from  the  two  observed 
weights  of  product  and  substance. 

Official  Rule. 

Sometimes  it  is  Krule  officially  given,  independent  of  the 
case  in  hand.  I  am  afraid  this  is  quite  often  the  only  limit 
observed. 

I  vividly  recollect  how,  more  than  thirty  years  ago,  I 
noticed  the  specific  gravity  of  limestone  specimens  marked 
to  seven  decimal  places  each,  without  fail. 

This  was  in  a  great  scientific  military  establishment — 
supported  by  Uncle  Sam. 

Knowing  how  sensitive  military  scientists  are,  I  ran  my 
eye  over  a  large  number  of  the  samples  of  buiding  stones, 
con-esponding  samples  of  which  were  known  to  be  in  my 
own  hand  for  investigation,  before  I  dared  ask  for  "  more 
light." 


ERRORS    OF   WEIGHING.  45 

Upon  putting  my  question  in  the  most  modest  form  as  a 
request  for  information,  I  was  informed  that  these  specific 
gravities  were  calculated  by  means  of  seven  place  logarithms. 

Seriously  and  most  earnestly  I  here  am  compelled  to 
declare,  that  much  of  the  vaunted  high  accuracy  of  the 
so-called  exact  science  of  to-day  in  our  laboratories,  our 
publications  and  our  academies  of  sciences,  sciences  has  no 
better  foundation  in  nature  or  fact  than  had  the  last  four  of 
the  seven  decimals  given  in  beautiful  and  distinct  writing  on 
the  labels  of  common  building  stones  in  one  of  the  military 
science  shops  of  the  great  United  States  of  America. 

True  and  Sham  Accuracy. 

But  if  we  would  lift  the  fog  that  has  settled  over  the  true 
values  of  the  fundamental  data  of  chemistry,  the  atomic 
weights  of  the  elements,  since  the  first  publication  of  the 
misleading  and  muddled  work  of  Stas,  we  must  learn  to  dis- 
tinguish between  true  accuracy  and  sham  accuracy. 

We  must  again  rely  on  the  chemist  and  not  merely  on 
the  balance  and  the  weights. 

If  Ramsay,  with  the  finest  balance  oscillating  to  the  ten 
millionth  of  the  gramme,  did  not  get  as  good  and  true  a 
chemical  result  as  did  Berzilius  eighty  years  earlier  by 
means  of  a  balance  not  better  than  the  prescription  balance 
of  common  American  drug  stores,  we  must  cease  to  judge 
by  the  apparatus  and  again  demand  the  work  of  a  true 
chemist. 

The  Number  of  Decimals. 

And  how  shall  we  limit  our  number  of  decimals  in  the 
calculation? 

Any  one  can  answer  this  question,  both  theoretically  and 
practically. 

The  theoretical  answer  can  be  readily  given  by  our  gen- 
eral mode  of  calculation  stated  before.  See  pp.  29-32. 

The  practical  answer  in  this  case  is  the  simplest  possible. 
It  is  useless  to  give  more  decimals  than  one  beyond  the  first 
varying  digit. 


46  THE    ERRORS    OF    PRECISION. 


In  the  case  of  the  water  of  crystallization,  the  third 
decimal  in  the  analytical  ratio  of  Ramsay  and  Aston  varied 
from  i  to  2.  Hence  only  four  decimals  should  have  been 
recorded,  instead  of  six. 

Or  to  avoid  misunderstanding,  the  tenth  of  per  cent  of 
water  of  crystallization  running  from  one  to  two,  only  one 
decimal  more  ought  to  have  been  given,  the  hundredth  of  a 
per  cent — as  decidedly  uncertain. 

A  Fine  Probable  Error. 

I  cannot  help  adding,  as  a  fine  commentary  to  the  above, 
the  "  probable  error  "  calculated  by  Clarke,  our  government 
chief  chemist,  in  his  <e  Constants  of  Nature,"  published  by 
our  Smithsonian  Institution  in  1897. 

On  page  172  the  probable  error  of  this  result  is  given  as 
0.0086  per  cent,  or  let  us  plain  chemists  put  it  at  0.009  Per 
cent  or  0.00009  per  unit  (our  ratio). 

How  easily  our  government  chemist,  by  a  little  mechani- 
cal calculation  converts  experimental  results  uncertain  in 
the  third  decimal  to  fine  work  with  a  probable  error  less 
than  a  unit  in  the  fourth  place! 

No  wonder  that  even  students  in  our  universities  are 
making  atomic  weight  determinations.  Their  balances  and 
weights  are  finer  than  those  Berzelius  used — and  they  can  also 
calculate  the  "probable  error"  of  their  result,  something 
that  Berzelius  did  not  do. 

And  as  A.  Cornu  of  Paris  (Nov.  16,  1894),  wrote  me  in  a 

letter  very  commendatory  of  my  "True  Atomic  Weights," 

ti  the  extension  of  the  method  of  the  least  squares  has 

"  unfortunately  persuaded   many  people   that  syste- 

11  matic  errors  do  not  exist  any  more!" 

We  have  given  evidence  of  the  existence  and  great  mag- 
nitude of  just  such  errors. 

IX.     MINUTE  CHEMICAL  ERRORS. 

Having  critically  considered  the  common  process  of 
reduction  of  the  experimental  work  of  atomic  weight  deter- 
minations, we  may  next  point  out  the  leading  chemical 
features  of  this  work. 


MINUTE  CHEMICAL  ERRORS.  47 


This  will  be  necessary  because  we  must  obtain  some  defi- 
nite knowledge  of  the  general  chemical  principles  involved 
in  this  experimental  work  in  order  that  we  may  be  able  to 
judge  of  the  relative  value  of  the  different  processes  in  use. 

This  somewhat  systematic  view  of  the  experimental 
chemical  work  is  also  necessary  because  our  general  works  on 
chemistry  give  almost  no  information  on  this  great  subject 
of  the  determination  of  atomic  weights. 

This  chemical  work  consists  in  the  following  operations: 
I,  selection  or  preparation  of  the  material;  II,  performing 
the  chemical  operation  whereby  the  new  material  is 
obtained;  and  III,  determining  the  weight  of  these  two 
materials. 

It  has  already  been  stated,  that  the  material  must  be 
absolutely  pure,  the  reaction  or  process  complete  and  defi- 
nite, and  the  weighings  accurate. 

As  only  definite  chemical  compounds  can  undergo 
definite  chemical  reactions,  the  starting  material  must  be  a 
definite  chemical  compound  or  element,  and  the  material 
resulting  from  the  reaction  must  also  be  of  such  chemical 
nature. 

The  necessity  of  obtaining  the  weight  of  these  two  mate- 
rials greatly  limits  the  choice  of  compounds  that  can  be 
used.  Hygroscopic,  efflorescent  and  otherwise  readily 
changeable  materials  must  be  excluded ;  for  they  cannot  be 
handled  and  weighed  with  precision. 

It  is  very  true  that  Stas  and  many  of  his  imitators  have 
by  ''skill"  fancied  to  overcome  these  difficulties;  but  we 
shall  see,  that  these  attempts  were  disastrous  to  chemistry. 

This  is  precisely  what  Berzelius  warned  against  in  his 
Rule  of  1814,  printed  p.  3.  He  means  to  say  that  the 
completing  of  the  reaction  must  depend  upon  the  chemical 
and  physical  properties  of  the  materials  themselves,  and  not 
on  the  skill  of  the  operating  chemist. 

Unfortunately,  our  modern  chemist  tries  to  show  off  as  a 
sort  of  chemical  acrobat  or  virtuoso,  able  to  do  something 
very  difficult,  while  Berzelius  and  his  school  skillfully  used 
the  properties  of  matter  with  the  sole  aim  of  obtaining  true 
and  reliable  results. 


48  THE   ERRORS    OF   PRECISION. 

The  starting  material  must  be  an  element  or  simple 
compound,  strictly  pure  and  accurately  weighable. 

Our  Standard  of  Matter. 

The  diamond  is  pre-eminently  such  a  material.  It  has 
been  selected  by  us  as  the  standard  of  matter  for  all  atomic 
weight  determinations.  Comptes  Rendus,  T.  117,  pp.  1075- 
1078;  1893.  True  Atomic  Weights,  p.  174;  1894. 

The  properties  peculiar  to  the  diamond  which  make  it 
almost  the  only  substance  fit  to  be  taken  as  standard  of 
matter  are  its  absolute  resistance  to  all  ordinary  physical  and 
chemical  agencies — making  it  weighable  with  highest  pre- 
cision; and  its  practically  absolute  chemical  purity,  the 
foreign  matter  present  being  incombustible  and  remaining 
as  a  perfectly  fixed,  exactly  weighable  ash  at  the  close  of  the 
combustion.  See  p.  39. 

The  diamond  occurs  native  in  perfectly  suitable  speci- 
mens, of  not  an  excessive  cost,  considering  its  almost  ideal 
qualities  as  the  fundamental  standard  of  matter  for  chemical 
science. 

As  the  diamond  will  stand  the  action  of  even  aqua  regia 
and  quite  a  considerable  degree  of  temperature  without 
change,  all  accessory  accretions  may  be  completely  removed. 

The  atomic  weight  of  the  carbon  of  the  pure  diamond 
we  take  as  12  exactly. 

It  is  most  essential  to  state  plainly  already  at  this  point, 
that  no  form  of  carbon  can  be  used  for  this  purpose  of  a 
standard  of  matter,  other  than  the  diamond.  Even  graphite 
cannot  be  employed,  and  artificial  forms  of  so-called  carbon 
are  entirely  out  of  the  question.  These  forms  of  carbon  all 
lack  one  or  the  other  of  the  properties  of  the  diamond. 
Already  Dumas  noticed  that  they  cannot  be  weighed  with 
accuracy.  We  shall  come  back  to  this  subject  under  carbon. 

Pure  oxygen  we  can  obtain  by  proper  washing  and  drying. 

The  combustion  of  the  pure  diamond  in  pure  oxygen 
gives  only  carbon  dioxide  gas  which  is  completely  absorbable 
and  accurately  weighable,  as  was  first  practiced  by  Dumas  in 
1840.  True  Atomic  Weights,  pp.  19-22;  1894.  Also  p.  39, 
supra. 


MINUTE  CHEMICAL  ERRORS. 


49 


The  weight  of  the  product,  here  CO2,  divided  by  the 
material  used,  here  the  diamond — carbon,  C,  each  one 
determined  by  actual  weighing,  gives  us  the  analytical  ratio, 
here  n  to  3  with  almost  mathematical  exactness,  as  we  shall 
show  in  a  subsequent  chapter  from  the  record;  also  p.  39. 

In  this  process  of  almost  ideal  perfection  we  have  one 
type  of  excellent  atomic  weight  determination. 

As  result  hereof  we  find  oxygen  16,  exactly,  as  we  shall 
show.  Thus  practically,  we  have  in  C=i2  as  diamond 
standard  of  matter  also  found  the  old  Berzelian  Oxygen 
Standard  at  16  exactly. 

Oxidation  of  Metals. 

Some  metals  can  be  chemically  produced  in  an  almo.st 
absolutely  pure  state,  permanent  in  dry  air,  hence  accurately 
weighable. 

Some  of  these  metals  can,  at  a  moderate  degree  of  heat, 
be  completely  converted  into  a  definite,  fixed  oxide,  which 
therefore  is  also  exactly  weighable. 

Hence  such  metals  are  suitable  for  very  accurate  atomic 
weight  determinations  by  such  a  process  of  oxidation. 

Some  of  these  metals,  such  as  tin,  may,  by  heating  in  a 
current  of  hydrogen,  again  be  reduced  to  the  metallic  state, 
and  thus  permit  a  double  determination  of  their  atomic 
weight. 

These  methods  of  direct  oxidation  and  reduction  are  among 
the  best,  most  direct  and  most  accurate  of  all  methods  of 
atomic  weight  determinations,  and  were  used  and  perfected 
by  Berzelius  and  his  disciples  during  the  first  quarter  of  the 
nineteenth  century. 

These  standard  methods  of  atomic  weight  determinations 
we  shall  find  to  be  infinitely  more  accurate  than  many  of  the 
new  methods. 

Dry  Way  Processes,  and  Crystals. 

In  general,  all  dry  way  processes  are  infinitely  preferable 
to  wet  way  processes. 

Erdmann  and  Marchand  weighed  the  mercuric  oxide  and 
distilled  the  mercury  over  by  means  of  heat,  collecting  the 


THE    ERRORS    OF    PRECISION. 


last  trace  of  the  vapor  of  mercury  by  a  gold  leaf.  The 
results  obtained  by  this  dry  way  process  are  among  the  very 
best  in  the  annals  of  chemistry,  as  we  shall  find. 

Here  the  analytical  ratio  is  the  weight  of  the  mercury 
collected,  divided  by  the  weight  of  the  oxide  taken. 

Another  class  of  dry  way  processes  we  have  in  simple 
ignition  or  dissociation. 

The  purity  of  the  material  used  is  generally  depending 
upon  the  process  of  crystallization  and  careful  re-crystalli- 
zation. 

Thus  pure  blue  vitriol  will  leave  the  fixed  black  oxide  of 
copper,  as  practiced  by  Richards. 

Ammonium  Alum  leaves  a  fixed  residue  of  Alumina 
(Mallet). 

The  remarkable  finely  crystallized  Chloro — and  Bromo — 
Platinates  leave  upon  ignition  pure  platinum  direct  or  after 
washing  the  residue  with  water  according  as  the  Ammonium 
or  Potassium  Salt  has  been  used.  Most  excellent  determina- 
tions have  been  made  in  this  line  by  Seubert  and  Halberstadt. 

The  related  Potassium  Bromo-Aurate  has  furnished,  by 
Kriiss,  the  most  accurate  determination  of  the  atomic 
weight  of  gold. 

The  ignition  of  purest  Iceland  Spar  gave  us  the  most 
reliable  determination  of  the  atomic  weight  of  calcium 
(Erdmann  and  Marchand). 

We  shall  find  that  the  ignition  of  the  purest  native 
magnesite  (from  Frankenstein)  has  given  us,  in  the  determi- 
nations-of  Scheerer,  really  the  true  atomic  weight  of  mag- 
nesium. 

All  these  dry  way  processes  are  simple,  direct,  complete, 
and  permit  accurate  weighings.  They  are  necessarily  the 
most  reliable,  although  modern  chemists  have  not  estimated 
these  processes  properly. 

The  starting  material,  the  compound  used,  is  often  either 
some  native  or  artificial  crystal. 

The  purity  of  the  starting  material  thus  is  dependent  upon 
the  crystallizing  power. 

Crystallized  minerals,  such   as  quartz   and   calcite — and 


LARGER    CHEMICAL    ERRORS.  51 

crystallized  salts,  such  as  alum  and  the  vitriols,  have  been 
known  from  the  earliest  times. 

These  bodies  are  the  first  indications  of  definite  chem- 
ical compounds,  therefore  the  very  foundation  stones  of 
chemistry. 

The  power  of  crystallization  also  permits  us  to  obtain 
chemically  pure  materials  for  our  atomic  weight  determina- 
tions. 

We  may  safely  assert  that  chemical  science  depends  more 
on  this  power  of  crystallization  than  on  any  one  other; 
without  this  power,  the  very  idea  of  a  chemical  compound 
would  perhaps  not  yet  have  been  acquired. 

The  native  and  artificial  crystals  presented  and  produced 
the  idea  of  chemical  individuals  and  compounds  first  in 
our  mind. 

The  most  marvelous  of  all  crystals,  the  diamond,  we 
have  found  to  be  the  most,  if  not  the  only  suitable  standard 
of  matter  for  all  atomic  weight  determinations. 

The  crystallized  carbides,  produced  by  the  electric  fur- 
nace of  Moissan,  were  pointed  out  by  us  in  1894,  as  most 
important  materials  fit  for  exact  work  to  connect  elements 
directly  with  carbon.  (True  Atomic  Weights,  pp.  175-176; 

1894.) 

This  process  has  been  actually  used  by  Henri  Gautier  in 
the  Laboratory  of  Moissan,  as  will  be  stated  in  the  chapter 
on  the  determination  of  the  atomic  weight  of  boron. 

This  method  is  quite  general  and  will  become  of  great 
value  by  directly  linking  the  atomic  weight  of  many  elements 
to  that  of  carbon. 

It  is  strange  that  this  method  was  used  by  Moissan  with- 
out mentioning  its  origin. 

X.     LARGER  CHEMICAL  ERRORS. 

In  modern  days  we  have  learnt  to  produce  another  class 
of  bodies  in  almost  chemically  pure  form,  namely  those 
bodies  which  are  volatile  enough  to  be  distilled. 

Even  silver  has  been  distilled  in  the  lime  retort  by  the 
heat  of  the  oxyhydrogen  blowpipe  for  use  in  atomic  weight 


52  THE    ERRORS    OF    PRECISION. 

determinations;  but  we  here  refer  to  much  more  volatile 
substances  which  permit  their  distillation  at  a  temperature 
readily  controlled. 

Such  are  especially  the  chlorides  and  bromides  of  certain 
elements  not  readily  subjected  to  dry  way  oxidation  and 
reduction. 

We  refer  here  to  the  use  of  silicon  chloride  and  bromide 
by  Thorpe  and  Young  and  the  corresponding  compounds  of 
boron  by  Henri  Gautier. 

The  silicon  bromide  used  by  Thorpe  and  Young  boiled 
at  the  fixed  temperature  of  153  degrees. 

These  chlorides  react  with  water,  producing  the  oxide 
and  the  corresponding  acid. 

The  insoluble  oxide  is  generally  separated  in  a  weighable 
form,  and  the  acid  may  be  determined  by  converting  it  into 
the  weighable  silver  compound. 

This  mere  statement  of  the  process  is  sufficient  to  show 
that  it  is  necessarily  much  inferior  to  the  ordinary  dry  way 
processes. 

As  unfortunately  great  errors  have  crept  into  chemistry 
by  the  silver  process — especially  when  the  chloride  is  con- 
cerned— these  apparently  very  fine  methods  will  be  found  to 
be  of  a  secondary  value  only. 

The  silver  process  here  referred  to  is  the  comparison 
with  weighed  amounts  of  pure  silver,  not  the  volumetric 
process  proper,  which  latter  we  shall  mention  further  on. 

Other  wet  way  processes  terminating  with  dry  substances 
and  therefore  permitting  the  actual  weighing  of  the  final 
products,  have  been  introduced  during  the  last  quarter  of  a 
century. 

Good  Special  Methods. 

One  of  the  most  interesting  and  accurate  of  these  pro- 
cesses is  the  conversion  of  anhydrous  borax  into  sodium 
chloride  by  distillation  with  muriatic  acid  and  methyl 
alcohol.  Sodium  chloride  is  left  and  weighed. 

It  can  be  objected,  that  this  process  is  somewhat  indirect, 
since  the  product  does  not  itself  contain  the  element  in 
question,  boron. 


LARGER    CHEMICAL    ERRORS.  53 

But  the  product  is  in  excellently  weighable  condition, 
and  contains  the  metal  wherewith  boron  was  combined  in 
the  substance,  borax. 

Hence  the  value  of  the  process  depends  entirely  on  the 
completeness  of  the  chemical  reaction  used. 

Sometimes  it  is  almost  impossible  to  obtain  an  exactly 
weighable  substance  for  the  initial  material,  because  of  the 
difficulty  of  removing  definitely  all  water  of  crystallization 
or  some  other  secondary  constituent. 

If  now  that  compound  permits  the  exact  determination 
of  the  element  sought  and  some  other  of  which  the  atomic 
weight  is  known,  good  atomic  weight  determinations  are 
possible,  though  the  original  substance  cannot  be  weighed. 

The  most  valuable  application  of  this  method  we  find  in 
the  splendid  work  of  E.  Maumene"  on  silver  acetate.  True 
Atomic  Weights,  p.  196;  1894. 

He  determined  the  silver  and  carbon  in  this  compound. 
The  silver  as  metallic  residue,  the  carbon  as  dioxide. 

We  shall  find  this  the  only  strictly  unobjectionable  deter- 
mination of  the  atomic  weight  of  silver. 

The  method  used  for  the  determination  of  the  atomic 
weight  of  uranium  in  the  laboratory  of  Professor  Armand 
Gautier  is  of  the  same  general  character.  In  this  case,  the 
atomic  weight  of  uranium  is  expressed  in  that  of  nitrogen. 
See  pp.  35-36  above. 

Methods  Giving  Variable  Results. 

We  have  not  yet  referred  to  the  conversion  of  a  weighed 
amount  of  a  pure  metal  into  a  definite  salt  by  means  of  an 
acid. 

In  this  way  Berzelius  produced  lead  sulphate,  and  Stas 
obtained  also  the  nitrate  of  lead  and  of  silver. 

Stas  has  laid  great  stress  upon  these  syntheses  of  silver 
and  lead  nitrate.  He  even  challenged  the  chemists  of  the 
world  to  show  that  his  results  were  not  exact.  True  Atomic 
Weights,  p.  34. 

But  his  own  data  show  that  this  method  is  not  applicable 
to  atomic  weight  determinations  for  silver  and  lead. 


54  THE    ERRORS    OF    PRECISION. 

This  has  been  fully  shown  in  our  True  Atomic  Weights, 
1894,  and  in  the  Comptes  Rendus,  T.  116,  pp.  431-433;  1893. 
We  shall  again  demonstrate  it  in  this  work,  but  shall  not 
enter  into  any  detail  at  this  point. 

When  the  silver  nitrate  produced  per  unit  of  weight  of 
the  metal  quite  notably  varies  with  the  amount  of  silver 
operated  upon,  and  even  constantly  differs  according  as  the 
nitrate  is  "  dried  "  or  "  fused,"  the  process  used  is  simply 
not  fit  for  the  determination  of  atomic  weights. 

Methods  of  a  dubious  value  are  those  wet  way  processes 
in  which  a  precipitate  is  separated  and  weighed.  All 
chemists  understand  that  these  methods  are  not  quite  exact 
for  atomic  weight  determinations. 

Neither  barium  sulphate  nor  silver  chloride  is  absolutely 
insoluble  in  the  liquid  used,  nor  absolutely  free  from  foreign 
matter. 

Processes  of  this  kind  must  be  expected  to  give  values 
not  quite  exact. 

False  Methods. 

Even  common  acidimetric  tests  have  been  applied  for 
atomic  weight  determinations,  by  Julius  Thomsen  of  Copen- 
hagen, and  Richards  of  Harvard. 

Richards  tried  to  determine  the  sulphuric  acid  left  after 
the  electrolysis  of  blue  vitriol  by  this  method — and  got  won- 
derful results,  since  he  overlooked  that  a  part  had  changed 
to  persulphuric  acid,  which  has  only  half  the  saturating 
capacity.  See  True  Atomic  Weights,  pp.  135-136. 

Here  also  must  be  mentioned  the  volumetric  process  of 
Rimbach  (1893)  on  borax  with  hydrogen  chloride,  using 
methyl  orange  as  indicator. 

It  is  really  strange  that  chemists  can  so  far  forget  the 
fundamental  requirements  of  atomic  weight  determinations 
as  to  think  of  volumetric  processes  of  this  kind. 

But  there  is  one  wet  way  process  which  has  caused  many 
errors  to  take  deep  root  in  the  chemistry  of  atomic  weight 
determination.  Together  with  the  Stasian  syntheses  of  the 
nitrates,  the  volumetric  silver  chloride  process  has  muddled 
this  part  of  the  science  for  almost  forty  years. 


LARGER  CHEMICAL  ERRORS.  55 

It  will  be  necessary  to  say  a  few  words  about  this  process 
by  way  of  a  general  protest  against  its  common  use. 

The  silver  chloride  volumetric  process  is  most  valuable  in 
technical  analyses,  and  nothing  here  to  be  said  is  intended 
to  reflect  upon  the  method  of  Gay-Lussac  and  Alohr  when 
restricted  to  technical  problems. 

But  we  must  insist  that  this  method  is  unfit  for  the  work 
of  atomic  weight  determinations.  See  True  Atomic  Weights, 
pp.  121-128. 

In  order  to  keep  all  the  silver  in  the  precipitate,  there 
must  be  an  excess  of  the  chloride.  But  this  solution  then 
reacts  again  with  a  drop  of  silver  solution. 

If  the  solution  gives  no  further  reaction  with  silver,  it  will 
again  react  upon  the  addition  of  a  chloride. 

Clearly,  the  silver  chloride  precipitate  is  held  down  by 
an  excess  of  the  soluble  chloride;  the  amount  of  silver  is  in 
no  fixed  proportion  to  the  amount  of  chloride  in  the  liquid. 

These  facts  were  fully  presented  by  Mulder,  and  have 
been  admitted  by  Stas,  who  supposed  that  the  mean  between 
the  silver  and  chloride  limit  marks  the  true  compound. 

We  have  no  inclination  to  consider  fine  spun  imagination 
such  as  this  one  of  Stas  or  the  apparent  "  ion  "-philosophy 
of  Hoitsema  presented  in  Ostwald's  Zeitschrift  (XX,  272- 
282;  1896). 

It  is  sufficient  for  us  to  know  that  the  chlorine  and  the 
silver  are  not  present  in  fixed,  definite  proportion  in  this 
process,  but  vary  very  greatly. 

We  are  tired  of  being  called  to  facts,  when  the  facts  are 
imaginations  and  dreams  in  the  head  of  so-called  exact 
chemists. 

Chemists  must  cease  to  take  the  fancies  of  Stas  and  his 
school  as  facts. 

We  shall  not  discuss  this  point,  but  insist  on  the  facts. 

It  was  Pelouze,  about  1845,  who  introduced  the  volumetric 
silver  chloride  process  into  atomic  weight  determinations. 

This  ready  method  was  unfortunately  used  extensively  by 
Dumas  up  to  the  time  when  Stas  began  his  pretentious  work. 


56  THE    ERRORS    OF    PRECISION. 

Louis  Henry  of  Louvain. 

How  the  reputation  of  the  work  of  Stas  is  now  being 
kept  up,  we  must  show  by  one  of  the  most  notorious  exam- 
ples, which  also  will  show,  how  miserable  the  case  must  be 
when  such  methods  are  resorted  to. 

The  school  of  Stas  has  wrapped  this  part  of  our  science 
in  a  dense  cloud,  and  kept  the  atomic  weights  of  the  elements 
in  u  muddle. 

The  great  authorities  who  admired  the  show  of  decimals 
and  the  system  of  calculation — aped  after  mathematical 
patterns — have  continued  to  point  with  pride  to  the  "scien- 
tific work  of  Stas,"  of  the  Academy  of  Brussels. 

The  Academy  of  Sciences  of  Brussels  in  public  session 
(Dec.  17,  1899)  listened  with  admiration  to  an  address  by  its 
member  Louis  Henry  of  Louvain,  who  glorified  his  boyhood 
fellow  townsman  and  repeated  silly  criticisms  of  my  True 
Atomic  Weights  second  hand. 

This  address  was  published  by  the  Belgian  Academy  in 
elegant  form,  and  circulated  with  great  diligence.  Comptes 
Rendus,  T.  130,  p.  691. 

Upon  request  I  received  a  copy  from  the  author,  Professor 
Louis  Henry,  in  the  summer  of  1900. 

In  his  letter  of  transmission  he  disclaims  all  personal 
knowledge  about  the  branch  of  chemistry  in  question.  He 
also  states  that  he  had  not  read  my  work  himself. 

Having  read  his  address,  so  highly  applauded  by  the 
Academy  of  Sciences  of  Brussels,  I  am  personally  convinced 
of  the  absolute  truth  of  his  statement  in  his  letter  to  me, 
namely  that  he  does  not  personally  understand  the  subject 
of  atomic  weights  he  discusses,  nor  had  any  personal  knowl- 
edge of  my  book  which  he  condemns. 

If  Louis  Henry  were  simply  a  professor  of  chemistry  of 
the  Stasian  school,  I  would  take  such  an  occurrence  as  a 
matter  of  course. 

But  Louis  Henry  is  Professor  of  Chemistry  at  the  Jesuit 
University  of  Louvain. 


LARGER  CHEMICAL  ERRORS.  57 

That  a  Jesuit  rushes  ignorantly  to  the  defense  of  the  false 
doctrine  of  a  man  like  Stas,  simply  because  he  and  Stas 
were  boys  together,  is  the  remarkable  feature  of  this  case. 

In  order  to  avoid  any  misunderstanding  I  beg  to  add  that 
I  have  the  highest  respect  for  his  church  and  for  many  men 
of  his  order,  and  remember  with  especial  gratitude  the 
kindness  shown  my  earliest  contributions  to  science  in  the 
great  works  of  Father  Secchi  on  the  Sun  and  on  the  Unity 
of  the  Forces  of  Nature.  See  my  General  Chemistry,  1897, 
p.  29,  p.  239. 


PART  SECOND. 


The  Absolute  Atomic  Weight  of 
Ten  Leading  Elements. 


\.     OUR  METHOD  OF  DETERMINATION. 

Having  briefly  presented  the  mathematical  and  chemical 
methods  equally  required  in  the  making  of  any  atomic 
weight  determination,  and  having  indicated  some  of  the 
common  errors  committed  in  work  of  this  kind,  we  may 
begin  the  exposition  of  our  own  method  by  which  we  have 
obtained  the  absolute  values  of  the  atomic  weights  of  the 
chemical  elements. 

It  has  been  demonstrated  that  the  common  habit  of 
arbitrarily  (i  adopting  "  some  set  of  atomic  weights  in  the 
reduction  of  new  determinations  is  not  only  absolutely  irra- 
tional in  theory,  but  leads  to  gross  errors  in  practice. 

While  chemists  have  been  calculating  their  new  work  to 
the  second  and  third  decimal,  they  have,  by  the  above  prac- 
tice, started  out  with  errors  ten  and  even  a  hundred  times  as 
large.  See  pp.  33-37. 

Absolutely  Fixed  Points  Needed. 

As  in  triangulation  and  even  in  common  leveling,  per- 
fectly well  marked  starting  or  base  points  are  required  and 
carefully  made  often  at  great  labor  and  expense,  so  ive  must 
in  this  ftmdamental  ivork  in  chemistry  use  certain  absolutely 
fixed  data  in  all  our  calculations,  in  order  to  avoid  the  intro- 
duction of  errors  by  the  process  of  calculation  or  reduction. 

Now  such  data  we  have  in  the  indisputable  fact  that  the 
atomic  weights  of  all  elements  are  quite  near  whole  numbers, 
if  we  take  oxygen  as  16  exactly. 


OUR   METHOD    OF    DETERMINATION.  59 

In  a  few  cases,  as  for  copper  and  chlorine,  the  atomic 
weight  approaches  the  exact  half  unit. 

Moreover  these  atomic  weights  have  always  been  exten- 
sively used  under  the  name  of  common  atomic  weights. 

The  trite  atomic  weights  of  the  elements  are  experimen- 
tally known  to  differ  by  very  small  quantities,  if  at  all,  from 
these  common  values. 

This  is  the  plain,  unquestionable  result  of  all  the  chem- 
ical work  of  the  nineteenth  century  in  atomic  weight  deter- 
minations. 

Hence  the  real  problem  to  be  solved  is  the  determination 
of  the  exact,  but  small,  departure  of  the  true  atomic  weight 
from  these  common  values. 

Standard  Atomic  Weights. 

These  common  atomic  weights  of  whole  numbers  (or  in 
a  few  cases  exact  half  units)  shall  in  our  calculations  be 
taken  as  the  absolutely  fixed  standards  of  comparison. 

We  therefore  shall  call  them  the  standard  atomic  weights. 

The  following  table  gives  these  values,  carefully  revised 
by  myself,  and  in  alphabetical  order  of  the  chemical  symbol. 

Table  of  Standard  Atomic  Weights. 


A 

C 

12 

Fe 

56 

Ka39 

OS  I9! 

Se 

79 

Ur 

240 

Ag 

108 

Ca 

40 

Fl 

19 

La 

p    31 

Si 

28 

Va 

51 

Al 

27 

Cdii2 

Ga 

Li     7 

Pb207 

Sn 

118 

Wo  1  84 

As 

75 

Ce 

Ge 

Mg24 

Pd 

Sr 

Zn 

65 

Au 

197 

Cl 

35-5 

H 

i 

Mn55 

Pt  195 

Ta 

Zr 

90 

Ba 

'37 

Co 

He 

Mo  96 

Rb 

Te 

Be 

9 

Cr 

52      Hg2oo 

N     14 

Rh 

Th 

Bi 

208 

Cs 

In 

"3-5 

Na  23 

Ru 

Ti 

48 

Bo 

ii 

Cu 

63.5 

lo 

127 

Ni   58 

s    32 

Tl 

204 

Br 

So 

Di 

Ir 

193 

O     16 

Sb  120 

Tu 

(see  Wo 

•) 

The  mathematical  problem  to  be  solved  by  means  of  a 
thorough  discussion  of  all  the  actual  analyses  made  by  the 
chemists  of  the  nineteenth  century,  is  the  determination  of 
the  departure  of  the  trne  atomic  weights  from  these  fixed 
standard  values. 


60  ABSOLUTE   ATOMIC    WEIGHT. 

Surely,  if  we  establish,  from  the  actual  analyses,  the  exact 
value  of  such  departure,  we  shall  have  determined  the  true 
atomic  weight  for  any  given  element. 

To  most  chemists  this  may  seem  to  be  an  indirect  method, 
a  round  about  method;  but  a  moments  consideration  will 
convince  them  that  this  method  is  not  only  direct,  but  the 
only  mathematical  method  applicable  to  this  problem. 

Instead  of  complicating  the  calculation,  as  might  be 
supposed,  this  method  simplifies  all  calculations  to  a  won- 
derful degree. 

In  fact,  it  may  be  truly  said,  that  the  direct  solution  of 
this  problem  of  determining  the  true  atomic  weights  is 
impossible.  In  all  fairness,  the  chemists  who  for  a  century 
have  tried  their  best  by  this  method  and  now  see  the  whole 
subject  in  a  muddle  and  no  single  atomic  weight  truly 
known,  ought  to  be  ready  to  concede  that  their  direct  method- 
has  been  a  failure. 

Now,  wherein  is  our  indirect  method,  if  the  chemists 
will  call  it  such,  simpler  than  the  direct  method  thus  far 
employed  by  the  chemists  of  the  past  century  ? 

It  is  due  to  \hefact  that  the  deviations  from  the  standard 
values  being  known  to  be  small  quantities,  the  method  of 
calculation  becomes  extremely  simple,  because  second  and 
higher  powers  of  these  deviations  can  be  neglected. 

Method  of  Procedure. 

Let  us  now  see  how  this  our  method  can  be  applied  in 
the  most  simple  manner  for  the  determination  of  the  abso- 
lute and  true  atomic  weight  of  the  chemical  elements. 

By  the  analytical  operation  of  the  chemist,  the  element 
is  weighed  in  two  different  combinations,  the  one  having 
been  changed  into  the  other  without  loss  or  gain  as  near  as 
possible.  The  weighings  are  exact,  as  near  as  can  be. 

By  the  series  of  analytical  determinations,  that  is,  by  the 
laboratory  •work,  we  obtain  as  many  analytical  ratios  as 
determinations  have  been  made;  namely,  in  each  single 
case  we  divide  the  weight  of  the  substance  taken,  s,  by  the 
weight  or  the  product  formed,  p ;  the  quotient  is  our  ana- 


OUR    METHOD    OF    DETERMINATION'.  6l 

lytical  ratio,  a,  and  is  calculated  to  five  decimal  places, 
uniformly,  in  this  book. 

s:p  =  a  (i) 

Now  both  the  substance  and  the  product  are  definite,  well 
known  chemical  compounds,  as  pure  as  it  is  possible  for  the 
most  refined  chemical  art  to  produce  them. 

Hence  the  chemical  formula  of  these  compounds  is 
known. 

Taking  our  standard  atomic  -weights  for  these  symbols, 
we  shall  obtain  the  standard  atomic  -weight  of  both  the  sub- 
stance and  the  product. 

Let  us  represent  these  known  numbers  by  S  and  P,  then 
a  simple  division  will  give  us  the  standard  atomic  ratio, 
which  we  also  calculate  to  five  places: 

S:P  =  r  (2) 

All  the  rest  is  done  by  simply  comparing  the  analytical 
ratios  to  the  atomic  ratio,  always  using  the  units  in  the  fifth 
place  for  this  purpose. 

We  shall  soon  learn  that,  as  a  matter  of  fact,  the  analyti- 
cal excess 

e=za  —  r  (3) 

which  is  the  difference  between  the  analytical  and  our 
atomic  ratio,  is  very  small,  in  all  cases  where  the  analytical 
work  has  been  done  by  a  really  good  practical  chemist,  and 
where  the  method  used  has  been  a  good,  well  tested,  method. 

In  order  to  avoid  the  use  of  the  signs  minus  and  plus, 
always  awkward  in  non-mathematical  books,  we  shall  use 
the  common  terms  high  and  low  to  designate  the  character 
of  the  analytical  excess  e. 

Namely  high  if  it  is  greater,  and  loiv  if  it  is  less,  than  the 
atomic  ratio. 

Example :    Mercury. 

For  example,  mercuric  oxide  Hg  O  yields  metallic  mercury, 
Hg;  both  are  accurately  determined  under  the  conditions 
worked  out  by  Erdmann  and  Marchand  in  1844. 

The  standard  atomic  weights  are  Hg  =  200,  O  =  16, 
exactly.  Hence  the  reaction  determines  the  atomic  ratio  r 
as  follows:  Hg  :  Hg  O  =  200  :  216  =  0.92  593. 


62  ABSOLUTE   ATOMIC   WEIGHT. 

Here  the  atomic  ratio  is  r  =  o.92  593. 

To  secure  ready  comparisons,  we  shall  always  print  these 
ratios  by  leaving  an  n  -  space  between  the  second  and  the 
third  decimal. 

In  this  manner  the  five-place  decimal  becomes  easily 
readable,  the  first  tivo  decimals  represent  the  per  cent., 
the  last  three  decimals  represent  the  tenth,  hundredth  and 
thousandth  of  per  cent. 

We  know  of  no  chemical  work  where  the  sixth  decimal  is 
actually  determined,  or  significant.  Hence  we  never  shall 
give  more  than  five  decimals. 

In  the  first  determination  by  Erdmann  and  Marchand, 
they  obtained  75.9347  grammes  of  metallic  mercury  from 
82.0079  grammes  of  mercuric  oxide;  accordingly,  we  obtain 
the  analytical  ratio,  by  dividing  the  first  by  the  second 
weight,  a  =  0.92  594. 

Eviden^1  v,  in  this  their  first  determination,  the  analytical 
excess  is  /  high  according  to  our  mode  of  expression ;  for 
the  last  decimal  of  the  analytical  ratio  is  4,  while  in  the 
atomic  ratio  it  is  3. 

In  this  manner,  every  statement  of  fact  is  reduced  to  the 
simplest  possible  form,  and  easily  grasped  by  the  mind. 

Extremes  and  Range. 

We  shall  also  have  to  specially  consider  the  extremes  and 
the  range  of  the  analytical  ratios  of  any  series.  We  shall 
invariably  give  the  highest  first,  then  a  dash  as  minus  sign, 
followed  by  the  lo-west  value  observed.  A  semicolon  followed 
by  the  range  completes  the  statement.  Having  to  give  a 
multitude  of  results,  brevity  and  uniformity  of  representa- 
tion become  very  important. 

Since  in  good  series  of  determinations  there  are  no 
changes  in  the  first  two  decimals,  it  would  be  absurd  to 
incumber  the  record  therewith;  hence  we  only  print  the 
last  three  decimals  of  the  extremes. 

In  the  case  of  mercuric  oxide,  Erdmann  and  Marchand 
found  the  highest  analytical  ratio  0.92  606  and  the  lo-west 
0.92  594. 

Hence  we  record  simply  thus:     Extr.  606 — 594;   12. 


OUR    METHOD    OF    DETERMINATION".  63 

We  may  even  omit  the  Extr.  without  causing  any 
confusion. 

Determination  by  Sight. 

In  this  manner  it  becomes  a  simple  matter  of  inspection 
to  ascertain  hoiv  closely  the  actual  experimental  determina- 
tions, expressed  in  the  analytical  ratios,  approach  to  the 
atomic  ratio,  calculated  from  the  standard  atomic  weights. 

If  the  observed  ratios  differ  more  among  themselves  than 
from  the  atomic  ratio,  then  the  atomic  ratio  expresses  the 
facts  observed  within  the  limit  of  actual  determinations. 

In  this  way  we  shall  find  whether  or  not  the  standard 
atomic  weights  are  the  true  atomic  weights. 

If  the  analytical  ratios,  the  only  direct  expression  of  the 
observed  facts,  agree  within  the  limit  of  accuracy  obtained 
with  the  atomic  ratio,  then  the  true  and  the  standard  atomic 
weights  are  necessarily  the  same  within  the  limit  of  accu- 
racy obtained  by  the  actual  experimental  determinations 
made. 

//  is  in  this  simple  matter  of  fact  manner  that  tue  are  notv 
able  to  test  all  the  atomic  weight  determinations  made  during 
the  entire  nineteenth  century. 

Order  of  Procedure. 

We  shall  first  consider  the  most  important  of  all  elements, 
and  mainly  the  work  of  the  old  master,  Berzelius,  and  his 
school,  in  which  no  fancy  method  of  work  was  tolerated, 
and  when  simple  appliances  in  skillful  hands,  directed  by 
clear  heads  gave  results  that  still  challenge  admiration. 

Having  become  versed  in  this  work  and  acquired 
confidence  in  this  method,  we  shall  next  apply  it  to  the 
determinations  of  the  atomic  weight  of  boron  made  in  the 
best  Laboratories  of  London  and  Paris,  by  or  under  the 
immediate  direction  of  the  most  famous  operating  chemists 
of  the  present,  namely,  by  Ramsay  and  by  Moissan.  The 
work  of  the  latter  has  been  endorsed  by  the  Academy  of 
Sciences  of  Paris. 

We  shall  then  be  able  to  settle  the  question  of  the  true 


64  ABSOLUTE   ATOMIC    WEIGHT. 

atomic  weight  of  nitrogen,  the  corner  stone  of  the  system 
of  Stas  and  his  school. 

Then  will  follow  the  complete  record  of  all  experimental 
determinations  made  during  the  century,  in  alphabetic  order 
of  the  symbols  of  the  elements. 

Atomic  Weight  Calculation  Made  Easy. 

We  have  not  yet  shown  how  the  exact  atomic  weight  cor- 
responding to  any  given  analytical  ratio  can  instantly  be 
obtained  by  a  simple  mental  calculation.  This  is  due  to  the 
fact  that  we  here  really  are  making  use  of  a  very  refined 
method  of  mathematical  analysis,  although  we  wish  the 
chemical  reader  not  to  get  aware  of  it — for  he  might  shy. 

We  may  suppose  that  every  body  understands  that  all 
quantitative  relations  can  be  graphically  represented  by  a 
curve  drawn  to  scale,  and  that  at  any  point  of  such  a  curve 
the  element  of  the  curve  may  be  considered  a  straight  line 
(the  tangent)  for  a  distance  sufficiently  short. 

But  then  the  changes  of  the  variables,  the  co-ordinates, 
will  be  directly  proportional  within  that  limit. 

Hence,  for  small  changes  the  analytical  excess  tvill  be 
directly  proportional  to  the  corresponding  change  in  the  atomic 
IK}  eight. 

Now  nothing  is  easier  than  to  determine  and  express  this 
change  in  a  uniform  manner.  For  we  need  only  calculate 
the  atomic  ratio  say  for  an  increase  of  o.i  of  the  standard 
atomic  weight,  to  find  the  change  in  atomic  weight  corres- 
ponding to  any  analytical  excess. 

In  the  above  instance,  we  found  the  standard  atomic  ratio. 
Hg  :  Hg  O  =  200  :  216  =  0.92  593. 

Suppose   now   that   the  trite  atomic   weight  of  mercury 
were  200.1,  then  the  true  atomic  ratio  would  be 
Hg  :  Hg  O  =  200.1  :  216.1  =0.92  596. 

The  supposed  true  atomic  ratio  in  this  case  would  simply 
be  tl3  high "  as  compared  to  the  standard  atomic  ratio, 
using  our  simple  method  of  expression  for  the  excess  being 
3  units  in  the  fifth  place. 


OUR    METHOD    OF    DETERMINATION.  65 

We  may  also  express  this  result  by  saying 

"  Hg  =  200.1  gives  ratio  3  high  "  or  "  change  of  o.i  gives 
ratio  3  high  "  or  "  Chg.  3  high." 

Now,  in  the  first  determination  by  Erdmann  and 
Marchand,  they  found,  as  above  stated,  the  analytical  ratio 
0.92  594  or  "  i  high." 

Since  o.i  causes  3  high,  this  actual  "  i  high  "  corresponds 
to  our  one  third  of  o.i  or  0.03  on  the  atomic  weight  of 
mercury. 

That  is,  by  a  mere  glance  at  the  analytical  excess  (here 
i  high)  the  calculated  change  (always  for  o.i)  gives  the 
corresponding  departure  of  the  atomic  weight  from  the 
standard. 

In  this  case,  for  this  first  determination  by  Erdmann  and 
Marchand,  departure  is  0.03  from  the  standard  200,  so  that 
the  atomic  weight  of  mercury  exactly  corresponding  to  that 
first  determination  is  200.03. 

It  is  plain,  that  this  method  is  the  simplest  possible  for 
use,  calling  for  no  calculation  but  such  as  can  be  instantly 
made  mentally,  the  changes  for  o.i  having  been  given. 

It  is  the  well  known  method  of  proportional  parts,  used  in 
all  common  tables  of  sines,  tangents,  logarithms — we  extend 
it  to  the  atomic  weight  calculations. 

Of  course,  the  possibility  of  doing  this  depends  upon  the 
fact  that  the  true  atomic  weights  differ  very  little  from  our 
standard  atomic  "weights,  as  we  have  recognized  it  in  all  the 
analyses  of  the  nineteenth  century  so  far  as  the  chemists 
were  able,  and  therefore  their  methods  used,  reliable. 

Now,  if  absolutely  reliable  and  practically  concordant 
analyses  should  give  any  appreciable  analytical  excess,  not 
due  to  errors  of  work  or  process,  then  we  can  instantly,  by 
the  above  proportional  parts,  mentally  calculate  the  exact 
departure  d  of  the  true  atomic  -weight  t  from  our  standard 
atomic  -weight  s  and  obtain  t  =  s  -f-  d  (4) 

Standard  and  True  Atomic  Weights. 

I  may  already  here  remark,  that  we  shall  find  this  analyti- 
cal excess  e  entirely  within  the  limit  of  precision  attained. 


66  ABSOLUTE    ATOMIC    WEIGHT. 

zero,  and  consequently  also  the  departure  d  will  be  zero,  and 
therefore  the  true  atomic  weights  are  identical  ivith  our 
standard  atomic  -weights. 

This  is  the  grand  final  result  of  this,  our  analysis  of  all 
atomic  weight  determinations  made  up  to  the  present  date. 

Our  Earlier  Publications. 

In  conclusion,  we  may  be  permitted  to  point  out  the  steps 
which  have  led  us  up  to  this,  the  simplest  and  most  direct 
method,  which  I  trust  will  be  within  the  easy  comprehension 
and  application  of  every  student  of  chemistry  in  the  world- 

We  shall  simply  indicate  our  leading  publications 
concerned^ 

Our  work,  "  The  True  Atomic  Weights  of  the  Chemical 
Elements  and  the  Unity  of  Matter,  St.  Louis,  1894,"  gives 
essentially  this  method,  but  not  by  itself,  since  it  was  my  aim 
also  to  show  horv  eminent  analysts  had  been  mislead;  hence 
I  entered  upon  the  consideration  of  c(  the  trajectory  of 
errors"  and  the  mathematical  principles  of  "  the  limit 
method." 

Many  chemists,  unable  or  unwilling  to  understand  these 
collateral  matters,  have  shown  by  their  manner  that  I  was 
altogether  too  tender  in  this  fight  for  truth  against  error 
and  fraud. 

Hence  I  have,  in  this  present  work,  exclusively  devoted 
myself  to  show  in  a  manner  so  plain  that  the  wayfaring  man 
even  though  somewhat  foolish  need  not  err. 

Indeed  I  trust  every  chemist  will  see  that  the  results 
embodied  in  the  Stasian  methods  and  atomic  weights  are 
false,  and  that  as  a  matter  of  plain  fact,  our  standard 
atomic  -weights  are  the  true  atomic  -weights  'within  the  degree 
of  precision  actually  attained. 

The  entire  method,  in  its  essential  feature,  has  been 
printed  in  my  "  General  Method  for  the  calculation  of 
Atomic  Weights  from  the  Results  of  Chemical  Analysis  " 
in  the  Comptes  Rendus,  T.  116,  pp.  695-698;  1893,  which 
publication  was  followed  by  several  applications  of  the 
method,  in  other  issues  of  the  Comptes  Rendus. 


OUR    METH017    OF    DETERMINATION.  67 

The  general  mathematical  principles  upon  which  all  this 
depends  may  be  found  in  my  "  Method  of  Quantitative 
Induction,'*  Davenport,  1872,  and  much  of  the  detail  of 
calculations  involved  in  the  various  branches  of  this  work 
can  be  found  in  my  "  School  Laboratory  of  Physical  Science, 
vol.  I,  pp.  88-93;  and  pp.  93-99;  1871." 

It  was  that  very  work,  elementary  but  on  a  very  large 
scale,  carried  on  by  hundreds  of  students  under  my  care, 
that  made  me  understand  the  fallacies  of  probable  error, 
means,  etc.,  which  fallacies  constitute  the  dark  cloud  that 
has  been  resting  over  this  part  of  chemistry  since  Stas  began 
his  work,  and  infected  modern  chemists  with  the  horrible 
Morbus  Stasii. 

Baculus  vs.  Bacillus. 

In  my  "True  Atomic  Weights  "  I  tried  to  show  how  these 
victims  of  Morbus  Stasii  might  have  contracted  this  horrible 
disease  by  mistaking  the  Bacillus  thereof  for  some  benefi- 
cent agent  on  their  f<  Means  "  and  thus  encouraging  them  to 
commit  heinous  u  Probable  Errors "  far  beyond  their 
"Limits,"  thereby  getting  away  from  the  path  of  truth  on 
some  jag-like  u  trajectory  "  of  errors  and  deviations. 

As  this  my  kindness  of  heart  has  been  either  mistaken  or 
wilfully  misconstrued  by  the  victims  corrupted  in  their 
scientific  vitals  by  Morbus  Stasii,  I  have  become  convinced 
of  the  duty  to  use  a  plain,  strong  Baculus  energetically,  so  as 
to  drive  out  and  kill  the  Bacilli  from  the  old  victims,  and 
thus  to  prevent  the  young  chemists  of  the  world  from  infec- 
tion bv  the  horrible  Bacilli  of  Morbus  Stasii. 


THE  WEIGHT  OF  A  HALF  EAGLE. 

Before  actually  beginning  our  work  of  absolute  atomic 
weight  determinations,  it  may  be  advisable  to  supplement 
our  experimental  determination  of  the  weight  of  a  silver 
dollar  by  a  corresponding  experimental  determination  of 
some  Umted  States  Gold  Coin. 


68  ABSOLUTE   ATOMIC    WEIGHT. 

In  this  way  we  shall  see,  by  contrast,  the  effect  of  the 
greater  value  of  the  material  used  in  producing  much  more 
accurate  work  at  the  mint  and  a  consequent  greater  accuracy 
in  our  determination. 

This  corresponds  exactly  to  the  difference  between  ordi- 
nary chemical  analysis  and  atomic  weight  determinations. 

Roughly  speaking,  the  work  on  gold  coins  is  ten  times  as 
accurate  as  the  corresponding  work  on  the  silver  coins. 
Accordingly  we  have  to  weigh  to  the  milligramme. 

We  shall  restrict  ourselves  to  such  subjects  of  this  inves- 
tigation as  are  immediately  applicable  to  our  atomic  weight 
determinations. 

The  Mean  Weight  of  the  Half  Eagle. 

The  most  suitable  United  States  Gold  Coin  for  this  study 
is  the  Half  Eagle,  corresponding  to  the  English  Sovereign 
and  to  the  German  Twenty  Mark  coin.  Its  value  is  five 
dollars.  It  is  the  most  common  gold  coin  of  the  world. 

Drawing  six  such  coins  at  a  time  at  the  Bank,  I  have 
gradually  obtained  over  one  hundred  such  coins,  exactly  as 
they  were  current  during  the  first  six  months  of  this  year,  1901 . 

Each  coin  was  weighed  to  the  milligramme  and  the  mean 
of  each  lot  of  six  coins  was  calculated.  The  following  table 
gives  these  means  in  lots  of  sixes  in  the  order  of  time: 

8.298  —  8.328  —  8.346  —  8.359  —  8.331  —  8-337  —  8.340  - 
8.348  —  8.340  -  8.343  -  8.337  —  8.340  -  8.333  -  8.349  ~ 

8-339  -  8.327  —  8-334  - 

These  means  vary  quite  considerably.  The  first  is  the 
lowest,  8.298;  the  fourth  is  the  highest,  8.359.  The  range 
of  these  means  (of  six  each)  is  0.061  or  61  milligrammes. 

The  mean  weight,  of  six  each,  75  not  the  true  -weight,  very 
evidently. 

Let  us  see,  how  the  means  will  run  jf  we  combine  con- 
secutively two  of  the  groups,  so  as  to  get  the  means  of  12, 
then  of  24,  and  lastly  of  48  coins,  in  the  order  of  time, 
exactly  as  they  came  gradually  to  hand. 

The  means  of  twelve  coins  each  are:  8.313 — 8.352  — 
8-334  —  s-344  —  8.341  —  8.339  —  8-341  —  8.333- 


OCR    METHOD    OF    DETERMINATION. 


These  means  of  twelve  agree,  of  course,  much  better. 
The  first  is  the  lowest,  8.313;  the  second  is  the  highest, 
8.352.  The  range  is  0.039  °r  39  milligrammes;  only  about 
one  half  of  the  range  of  the  means  of  sixes. 

Combining  again  these  means  two  and  two  consecutively, 
we  obtain  the  me  an  weight  by  twenty  fours  of  Half  Eagles : 

8-333  —  8-339  —  8-340  —  8-337- 

These  agree  much  closer  again,  the  entire  range  being 
only  7  milligrammes. 

The  means,  by  forty  eight  Half  Eagles  are :  8.336  and 
8.338,  differing  by  only  2  milligrammes. 

The  mean  of  these  two  is  8.337  for  96  Half  Eagles  weighed. 

We  see  how  gradually  the  mean  becomes  more  fixed,  less 
subject  to  fluctuation,  as  the  number  of  individuals  used  for 
that  mean  increases. 

This  has  led  scientists  to  suppose,  that  we  obtain  a  higher 
accuracy  as  we  increase  the  number  of  observations. 

We  gain  concordance — expressible  by  a  small  probable 
error — but  we  have  not  approached  the  true  weight.  We 
shall  find  this  very  mean  22  milligrammes  low  as  a  very 
sound  constant  error. 

We  understand  the  fallacy  of  this  common  conclusion. 
The  same  number  of  Half  Eagles  in  another  city  would  not 
even  have  given  the  same  results,  since  other  years  of  coin- 
age most  likely  are  more  frequent  in  other  towns,  and  above 
all,  the  actual  weight  of  all  Half  Eagles  in  circulation  is  low* 
due  to  abrasion.  This  will  vary  greatly  in  time  and  rapidity 
of  circulation — and  for  gold  coin  also  with  the  greater  or 
less  care  exercised  in  withdrawing  light  coins  from  circula- 
tion. The  United  States  are  not  very  particular  in  this 
matter. 

Out  of  the  102  Half  Eagles  weighed,  the  following  were 
light  coins: 

8.235  —  8.235  —  8.257  —  8.270  —  8.280  —  8.282  —  8.284  — 
8.296  or  about  8  per  cent  below  8.300. 

As  a  matter  of  fact,  the  actual  coin  in  common  use  has  a 
larger  number  of  light  weights  than  this  percentage,  because 
the  teller  did  not  hand  me  any  coin  but  such  as  he  considered 
good  coin. 


•JO  ABSOLUTE    ATOMIC    WEIGHT. 


Frequency  of  Circulation. 

The  oldest  Half  Eagle  in  this  lot  was  of  1857,  the  latest 
of  1901.  The  entire  period  comprises  45  years. 

How  remarkably  varied  the  frequency  of  the  coin  is,  we 
found  again  for  gold  as  we  have  found  it  for  silver. 

The  year  1880  was  represented  by  9  coins,  1895  by  S; 
these  two  years  by  17  coins  out  of  102. 

The  year  1881  was  represented  by  20  coins,  the  year  1897 
by  21  coins;  these  two  years  represented  41  coins  out  of  a 
total  of  102. 

The  three  years:  1880,  1881  and  1897  were  represented  by 
50  coins.  In  other  words,  these  three  years  had  furnished 
half  of  all  coins  in  local  circulation ;  as  many  as  the  other 
42  years  taken  together! 

Amount  of  Abrasion. 

The  great  frequence  of  the  coins  of  the  two  years  iSSi 
and  1897  permits  us  to  obtain  an  estimate  of  the  amount  of 
abrasion. 

But  upon  looking  over  the  record  of  the  individual 
weights  of  the  Half  Eagles  of  1897  we  find  one  decidedly 
under-weight,  namely  8.235  only.  This  exceptionally 
"worn"  coin  must,  therefore,  be  laid  aside.  The  twenty 
remaining  coins  of  1897  range  from  8.322  to  8.370,  and  give 
a  mean  weight  of  8.357. 

The  twenty  Half  Eagles  of  1881  run  from  8.300  to  8.356 
and  give  a  mean  of  8.333. 

Hence,  in  the  16  years  from  1881  to  1897,  the  mean  wear 
of  20  Half  Eagles  has  amounted  to  24  milligrammes,  which 
is  i%  milligramme  per  year. 

Therefore,  a  new  Half  Eagle,  in  1901  should  weigh  about 
4/12  mgr<  more  than  the  mean  for  1897;  that  is  8.361 
grammes;  for  those  of  1897  have  only  been  3  years  in  circu- 
lation. 

We  have  obtained  only  one  single  Half  Eagle  of  1901 ;  it 
vreighed  8.356  grammes,  but  of  course,  had  lost  some  by 
abrasion  of  perhaps  half  a  year.  Besides,  the  mint  cannot 
produce  the  coin  equal,  even  of  gold,  to  the  milligramme. 


OUR    METHOD    OF    DETERMINATION.  >Jl 

Not  having  had  the  opportunity  of  weighing,  say  at  least 
20  such  coins,  fresh  from  the  mint,  I  cannot  state  the  actual 
tolerance.  I  think  it  must  amount  to  5  mgrs. 

Now,  by  Law,  each  Half  Eagle  is  to  weigh  129  grains, 
that  is  (to  nearest  milligramme)  8.359  grammes. 

Our  estimate,  based  upon  20  coins  each  of  1881  and  1897, 
gave  us  8.361  or  2  mgr.  in  excess  of  the  mean  legal  weight. 
I  think  we  have  done  well  enough.  It  corresponds  to  0.02 
on  an  atomic  weight  of  83. 

But  really,  we  did  not  determine  the  weight  directly. 
Direct  means  were  all  low,  for  iSSi  they  were  24  mgrs. 
below  the  mean  for  1897. 

These  two  years  gave  us  the  average  rate  of  -wear  or 
abrasion.  We  had  no  new  coin,  fresh  from  the  mint.  We 
supposed  that  the  rate  from  iSSi  to  1897  might  be  relied  on 
as  reasonably  true — and  hence  as  such  beyond  our  actual 
observation,  from  1897  to  the  present.  That  gave  us  the 
weight  8.361  at  the  mint;  the  law  says  it  shall  be  8.359. 

We  think  there  is  no  flaw  in  this  process — beyond  the 
desirability  of  larger  numbers  of  coin.  That  desirability  we 
admit.  In  fact,  we  admit  it  very  much. 


Criminal  Extrapolation. 

I  am  sorry  to  inform  my  readers,  that  they  have  been 
participants  in  a  great  scientific  crime,  the  crime  of  Extra- 
polation. 

Possibly  they  have  not  felt  their  scientific  conscience 
shiver;  that  would  be  too  bad,  according  to  the  opinion  of 
the  great  Stasian  critics,  referred  to  by  the  Olla  Podrida 
maker  for  the  Smithsonian  Institution,  on  page  6  of  his 
variable  Constants  of  1897. 

This  scientific  crime  of  extrapolation  consists  in  carry- 
ing experimental  data  beyond  the  immediate  field  for  which 
they  have  been  established. 

Thus  Stas  claims  he  found  14.04  for  nitrogen,  using  from 
about  100  to  400  grammes  of  silver,  converting  it  to  nitrate, 
fused  and  dried.  As  a  matter  of  fact  (True  Atomic  Weights, 


72  ABSOLUTE   ATOMIC   WEIGHT. 

p.  164)  the  corresponding  atomic  weights  of  nitrogen  varied 
all  the  way  from  14.05  to  14.10. 

Yet  the  Stasians,  referred  to  by  Clarke  above,  and  all 
other  Stasians  have  for  forty  years  extrapolated  the  atomic 
weight  of  nitrogen  for  any  weight  of  silver,  below  100 
grammes  and  above  400  grammes. 

In  fact,  the  Stasians,  are  hardened  criminals  in  this  mat- 
ter of  extrapolation  as  well  as  in  all  other  scientific  crimes. 

But  what  is  the  use  referring  to  such  things  any  longer? 
Why  suppose  it  possible  that  such  men,  u  blind  followers  of 
a  blind  guide,"  will  want  to  see  light?  Matt.  XXIII. 

Hence,  let  us  say  just  a  few  words  on  this  great  crime  of 
extrapolation  we  have  committed  above — and  exactly  in  the 
same  way  in  our  limit  method  of  our  True  Atomic  Weights 
of  1894 — and  at  almost  every  step  we  have  taken  in  our  life! 

Truly,  every  step  is  an  extrapolation ;  we  do  not  know 
that  the  laws  under  which  nature  worked  yesterday,  will 
remain  to-day.  We  do  not  know  that  the  sun  will  rise  to- 
morrow; if  we  say  it  will,  we  commit  the  horrible  crime  of 
extrapolation ! 

Come  to  think  of  it,  I  was  instructed  in  this  scientific  sin 
of  extrapolation  by  my  own  father ;  when  a  tnere  boy,  helping 
him  surveying  I  had  to  prolong  a  line  by  setting  stakes  in 
continuation  of  two  stakes — and  surely,  that  is  extrapolation 
of  the  worst  kind !  But  I  remember  I  did  it  well ;  probably 
natural  depravity  aided  by  parental  authority  and  instruc- 
tion. 

In  fact,  Euclid  and  other  old  Greek  heretics,  inculcate 
the  same  sinful  operations. 

It  is  really  grotesque  to  hear  "  the  blind  followers  of  the 
blind  guide  "  speak  of  the  crime  of  extrapolation  from  out 
of  the  mire  of  error  and  fraud  in  which  they  have  compla- 
cently weltered  like  a  lot  of  the  most  common  pachyderms 
of  these  prairies.  How  deliciously  dainty  the  Greek  sounds 
in  this  place. 

The  whole  Stasian  system  being  a  mysterious  muddle  of 
error  and  fraud,  varnished  with  a  pharisaical  show  of  sham- 
exactness,  is  true  to  itself  in  crying:  you  extrapoJatel 

When  Newton  is  said  to  have   thought  ( '  if  that  falling 


OUR   METHOD    OF   DETERMINATION.  73 

apple  had  come  from  the  moon  "  was  not  he  guilty  of  extra- 
polation? But  his  extrapolation  we  call  the  law  of  univer- 
sal gravitation,  and  it  has  been  so  called  for  two  centuries. 

If  you  have  the  truth,  you  may  extrapolate,  and  nature 
will  vindicate  you. 

But  if  you  are  surrounded  by  frauds  and  lies,  and  if  your 
very  soul  has  been  filled  by  this  contamination,  then  do  not 
get  out  of  the  miry  hole,  do  not  extrapolate  either  yourself 
or  anything  else  next  to  you,  for  the  Light  of  God's  Sun  will 
show  to  all  the  world  where  you  have  been  and  what  you 


The  Ratio  and  the  Excess. 

And  now  finally — let  us  apply  this  little  lesson  also  in  a 
strictly  formal  way,  in  numbers  and  by  calculation,  exactly 
as  if  we  had  an  "  absolute  "  atomic  weight  ratio  to  compare 
with  the  "  analytical  ratios"  of  actual  experience. 

Here  we  have  the  legal  weight  of  the  Half  Eagle  as  the 
absolute  standard  of  comparison,  namely  8.359  grammes. 
That  is  our  unit. 

We  have  also  the  present  actual  "mean  weight"  of  20 
Half  Eagles  of  1881,  being  8.333  grammes. 

We  have  likewise  the  actual  "  mean  weight "  of  20  Half 
Eagles  of  1897,  namely  8.357  grammes. 

We  had  to  reject  one  of  the  coins  of  1897  weighing  only 
8.235. 

We  finally  obtained — by  the  dreadfully  criminal  operation 
of  extrapolation — the  estimated  weight  of  a  new  Half  Eagle 
at  the  U.  S.  Mint  to  be  8.361,  although  we  regretfully  admit 
we  ne'r  had  such  an  one  in  hand. 

Let  us  calculate  the  corresponding  "  analytical  ratios" 
to  our  usual  five  places,  exactly  as  we  do  in  our  absolute 
atomic  weight  determinations.  That  will  give  us  a  very 
useful  case  of  comparison,  from  the  best  work  that  can  be 
done  at  the  mint,  on  the  most  valuable  material,  gold,  when 
again  picked  up  after  having  circulated  in  this  sinful  world 
at  large,  and  brought  upon  the  balance  and  tested  "  only  to 
the  milligramme,"  not  to  the  thousandth  of  the  milligramme ! 


74  ABSOLUTE   ATOMIC   WEIGHT. 

Actual  determinations  of  Half  Eagles  the   legal  weight 

being  taken  as  standard. 

Ratio.  Excess. 

20  Half  Eagles,  of  1881,  mean,  0.99  689  311  low. 

20  Half  Eagles,  of  1897,  mean,  0.99  976  24  low. 

Estimated  Weight  at  mint  i.oo  024  24  high. 

Legal  Weight  shall  be  i.oo  ooo  o  high. 

Rejected  coin  of  1897,  0.99  593  407  low. 

Amount  of  Abrasion,  16  years,  287 

hence  per  year,  18 

These  ratios  and  the  corresponding  excesses  are  very 
instructive.  They  show  7torv  very  rigid  the  comparison  of 
ratios  to  the  fifth  place  is.  Our  carefully  made  estimate  of 
the  new  coin  at  the  mint,  differing  only  by  2  milligrammes 
from  the  legal  standard,  here  shows  up  with  an  excess  of  24! 

We  see  also  that  the  "rejected"  coin  of  1897  fell  almost 
a  hundred  below  the  analytical  excess  of  the  mean  for  1881. 

Again,  it  appears  strikingly,  that  the  mean  weight  of  the 
gold  coin  gradually  approaches  the  legal  weight,  as  the  year 
of  coinage  is  less  and  less  distant  from  the  present.  The 
mean  of  1881  was  311  low,  that  of  1897  only  24  low. 

It  will  be  well  to  keep  these  cases  before  our  eyes  through- 
out the  study  of  this  work. 

II.     THE  ATOMIC  WEIGHT  OF  LEAD.     BERZELIUS. 

The  atomic  weight  of  lead  we  find  to  be  fully  established 
by  the  splendid  determinations  made  by  Berzelius  more  than 
seventy  years  ago.  The  many  later  determinations  have 
only  clouded  the  work  of  Berzelius  for  a  time.  We  there- 
fore put  his  name  at  the  head  of  this  section,  hoping  that 
hereafter  due  credit  will  be  given  this  our  great  master  for 
the  experimental  determinations  which  have  definitely  and 
permanently  established  the  true  atomic  weight  of  lead, 
the  metal  of  Saturn. 

A.    Lead  Carbonate  Ignited. 

The  earliest  work  of  Berzelius  I  can  find  recorded  on  the 
ignition  of  the  carbonate,  yielded  83.5  per  cent  of  lead 


LEAD.       BERZELIUS.  75 


oxide.  Philos.  Transact.  1814;  I  quote  from  Becker  (*)  p. 
71.  In  this  work  Berzelius  was  assisted  by  F.  H.  Wollaston. 

Per  unit  of  weight  of  lead  carbonate,  the  above  analysis 
gives  0.835  as  t*16  analytical  ratio. 

By  our  standard  atomic  weights,  Pb  Oa  C  =.  267  and 
PbO  —  223,  hence  our  atomic  ratio  is 

223  :  267  =  0.83  521 
and  rep'  jting  the  calculation  for  Pb  =  207.  i  we  find 

223.1  :  267.1=0.83  527 

which  is  6  higher.  Hence,  in  our  manner  of  expression, 
"Change  6  high  "  for  a  rise  of  o.i  in  the  atomic  weight  of 
lead. 

With  these  standard  ratios  the  actual  analytical  work  has 
to  be  compared. 

It  will  be  seen,  that  every  digit  of  the  analytical  ratio  of 
Berzelius  is  exact;  it  is  0.835.  An(*  this  dates  back  to  1814! 

We  find  a  second  double  determination  in  Meyer  and 
Seubert,  p.  128;  the  individual  values  are  never  quoted  by 
M.  &  S.,  they  only  give  aggregates.  We  can,  however,  trace 
the  exact  value  of  the  analytical  ratio. 

The  two  determinations  were  made  by  Berzelius  in  1817. 
He  took  10  grammes  of  carbonate  in  each  determination ; 
the  sum  of  lead  oxide  stated  is  16.6666  grammes. 

It  is  also  stated,  that  the  carbonate  was  found  to  contain 
a  trace  of  moisture ;  0.0225  in  the  first,  0.022  in  the  second, 
hence  0.0445  in  the  two.  Accordingly,  the  actual  amount  of 
real  lead  carbonate  was  not  20  grammes  exactly,  but  only 

19-9555- 

Dividing  the  amount  of  lead  oxide,  16.6666  by  the  amount 
of  lead  carbonate  19.9555  we  obtain  0.83  517  as  the  analytical 
ratio  of  Berzelius  two  analyses  of  1817. 

It  was  with  astonishment  that  I  beheld  this  number;  I 
revised  my  calculation,  being  unprepared  for  such  wonder- 
ful result. 


*The  so-called  Recalculators,  mainly  of  the  work  of  Stas,  but  also 
of  all  existing  atomic  weight  determinations,  are: 

Becker,  Meyer  and  Seubert,  Sebelien,  Clarke,  Ostwald,  Van  der 
Plaats,  and  Julius  Thomsen.  The  full  title  of  their  works  will  be  given 
at  some  one  place.  See  True  Atomic  Weights,  1894,  pp.  40-69. 


76  ABSOLUTE    ATOMIC    WEIGHT. 


I  have  just  revised  the  calculation  once  more,  before 
going  to  press;  the  result  is  exactly  as  stated. 

Simple  inspection  shows : 

Atomic  Ratio,     .          0.83  521  Hinrichs,   1901. 

Analytical  Ratio,     .     0.83  517  Berzelius,  1817. 

or,  in  our  parlance,       .     .  u  4.  low  "  only  in  the  fifth  place! 

Now  since  our  "  change  is  6  high  "  corresponding  to  o.i, 
the  atomic  weight  corresponding  to  the  two  determinations 
of  Berzelius,  made  in  1817,  is  £  or  %  of  o.i  low,  that  is  0.06 
low.  Accordingly  Pb  =  206.94. 

That  is,  the  experimental  determinations  of  Berzelius, 
taken  to  be  absolutely  exact,  would  correspond  to  the  atomic 
weight  of  lead  being  0.06  less  than  the  standard  207;  that  is 
Pb  =  206.94. 

But  Berzelius  himself  would  never  assume  absolute 
accuracy  for  his  work.  We  see  then,  that  his  oldest  deter- 
minations of  the  carbonate  on  record  agree  within  the  errors 
of  experiment  -with  the  standard  atomic  iveight  of  lead^  2Of. 

And  these  errors  of  experiment  we  have  found  to  be  not 
in  excess  of  0.06. 

Contrast  herewith  "  the  most  recent  work"  tabulated  by 
Clarke  in  his  edition  of  1897,  for  all  determinations  of  lead, 
ranging  2.5  units,  instead  of  0.06,  or  forty  times  the  uncer- 
tainty of  the  work  of  Berzelius  done  in  1817! 

B.    Lead  Oxide,  Wet  Way. 

In  the  earliest  determinations  on  the  conversion  of  lead 
into  lead  oxide,  Berzelius  generally  started  with  ten  grammes 
of  lead,  dissolved  the  same  in  a  glass  matrass  with  long  neck 
by  nitric  acid,  and  converted  the  resulting  nitrate  by  igni- 
tion into  the  oxide  in  the  same  matrass.  Special  variations 
in  the  general  process  we  need  not  refer  to  here. 

The  formula  of  this  process  is 

Pb  O  :  Pb  =  223  :  207  =.  i  .07  730. 

A  rise  of  o.i  in  the  atomic  weight  of  lead  causes  a  rise  of 
6  units  in  the  fifth  place  of  this  ratio;  that  is,  gives  6  high. 

Berzelius  found  ten  grammes  of  lead  to  gain  77.5  centi- 
grammes when  evaporated  in  the  same  glass  vessel,  and  78 


LEAD.       BERZELIL'S.  77 


cgr.  when    using   a   matrass    with    very  long   neck.     These 
results   were    first    published    by    him    in    1810.     (Sebelien, 

P-  M3)- 

Per  unit  we  get  the  analytical  ratio  1.07  750  (where  we 
have  to  supply  the  last  decimal  not  determined)  which  is  20 
high. 

The  actual  determinations  to  the  fourth  place,  which 
really  is  uncertain,  since  Berzelius  weighed  to  the  centi- 
gramme only  which  represents  the  third  place  in  our  ratio 
(centigramme  to  10  grammes  is  milligramme  to  the  gramme, 
or  third  place  in  our  ratio  per  unit). 

In  other  words,  Berzelius  found  the  oxide  exceeding  the 
amount  calculated  from  the  standard  atomic  weight  only 
two  centigrammes  in  excess  on  ten  grammes  of  lead ;  that  is, 
only  two  units  of  his  smallest  weights  used  on  his  balance. 

These  are  in  point  of  time,  the  earliest  of  all  atomic 
weight  determinations  of  any  heavy  metal ;  they  differ  from 
the  calculated  standard  by  only  two  units  in  a  thousand. 

C.     Lead  Oxide,  Dry  Way.    Earliest  Work. 

In  1812  he  published  in  the  Swedish  Afhandlingar  (vol. 
V,  see  Sebelien  p.  143)  his  first  reductions  of  pure  lead  oxide 
to  metallic  lead  by  heating  the  oxide  in  a  current  of  dry 
hydrogen  gas. 

This  is  a  chemical  process  of  a  much  higher  degree  of 
accuracy,  and  accordingly  we  find  that  his  determinations 
came  much  nearer  our  atomic  ratio. 

His  three  determinations,  referred  to  a  unit  weight  of 
lead,  gave  1.07  722;  1.07  723  and  1.07  740  as  analytical  ratios. 

These  ratios  are,  in  the  order  given,  8  low,  7  low  and 
10  high,  when  compared  to  our  atomic  ratio  above  given, 
namely  1.07  730. 

The  mean  of*  his  three  determinations  is  1.07  728  which  is 
only  2  low  (in  5th  place)  in  comparison  with  our  atomic  ratio. 

If  we  were  tc  consider  his  determinations  exact  to  the 
fifth  place  of  the  analytical  ratio,  the  atomic  weight  would 
be  I  or  £  of  one  tenth,  that  is  0.03  lower  than  the  standard 
207,  that  is  206.97. 


78  ABSOLUTE    ATOMIC    WEIGHT. 

Hence  we  can  assert  with  absolute  certainty  that  the  three 
determinations  of  Berzelius  made  by  reducing  lead  oxide  by 
hydrogen,  conform  to  the  full  limit  of  the  precision  of  his 
work  to  the  standard  atomic  weight  of  lead,  Pb  =  207. 

The  deviation  of  the  mean  is  only  2  low  (in  the  fifth 
place)  and  the  individual  determinations  fall  on  either  side, 
two  being  8  and  7  low,  one  being  10  high  (in  the  fifth  place). 

These  dry  way  determinations  of  Berzelius,  published  in 
1810  and  1812,  in  the  very  beginning  of  any  atomic  weight 
determinations,  fix  the  value  of  the  atomic  weight  of  lead  at 
207,  within  a  very  few  hundredths  as  a  barely  possible  un- 
certainty. 

This  is  the  record  of  our  Science.  Here  we  have  the 
earliest  record  of  the  work  done  by  the  greatest  master  in 
chemistry.  Every  true  chemist  should  be  proud  of  this 
record* 

Clarke  Falsifying  the  Record  of  Berzelius. 

It  is  therefore  with  inexpressible  disgust  and  contempt 
that  I  read,  at  the  very  opening  of  the  report  on  the  atomic 
weight  of  lead,  in  the  Smithsonian  publication  of  the  Chief 
Chemist  Clarke  (Constants  of  Nature,  Washington,  1897)  at 
the  top  of  page  127,  the  following  which,  every  reader  of  the 
historic  facts  just  given  will  recognize  as  barefaced  and 
absolute  falsehoods : 

"The  researches  of  Berzelius  upon  the  carbonate  and 
"  various  organic  salts  need  not  noiv  be  considered,  nor  is  it 
li  "worth  while  to  take  into  account  any  ivork  of  his  done  before 
"  the  year  1818." 

The  work  of  Berzelius  on  Lead  Carbonate  came  within  3 
units  in  the  fifth  place.  This  dry  way  work  on  the  oxide 
came  within  2  units  of  the  fifth  place  of  our  atomic  ratio. 

In  both  cases  this  means  the  determination  of  the  atomic 
weight  of  lead  to  be  207  within  a  possible  range  of  only 
three  hundredths  of  a  unit. 

At  the  close  of  his  chapter  on  lead,  this  same  Chief 
Chemist  Clarke  states  the  result  of  all  subsequent  work  on 
lead  to  run,  in  the  mean  values  over  t~Mo  and  one  half  units. 


LEAD.       BERZELIUS.  79 


This  is  a  range  much  in  excess  of  eighty  times  that  affect- 
ing the  determinations  of  Berzelius  made  from  1810  to  1814 
on  the  carbonate  and  the  oxide  of  lead. 

I  trust  that  every  young  chemist  will  read  the  protest 
against  Clarke's  garbling  the  record  of  Berzelius  I  have 
published  in  my  little  book  on  "  the  False  Atomic  Weights 
of  the  Smithsonian  Institution,"  pages  28  to  30. 

They  will,  I  am  sure,  agree  with  me  in  that  protest 
against  the  wilful  and  malicious  defilement  of  the  grand 
work  of  Berzelius. 

It  is  nothing  short  of  a  disgrace  that  the  highest  scien- 
tific officers  of  our  government  dare  produce  such  totally 
false  statements  of  the  record  of  Berzelius,  and  that  such 
disgraceful  falsehoods  are  published  with  the  endorsement 
of  the  Secretary  by  the  "Institution"  founded  for  the 
Increase  and  Diffusion  of  "Knowledge"  among  men,  and 
thus  sent  broadcast  to  chemists  everywhere  at  the  expense  of 
the  people  of  the  United  States. 

D.     Lead  Oxide,  Dry  Way.     Later  Work. 

The  work  of  Berzelius  which  we  shall  now  consider  is 
referred  to  his  Lehrbuch,  last  or  fifth  edition,  volume  III,  p. 
1218,  by  Clarke,  and  divided  into  two  parts  marked  "earlier" 
and  "latest"  results.  The  former  comprise  6  deter .nina- 
tions,  the  latter  3  determinations. 

Meyer  and  Seubert  (p.  28)  refer  to  the  same  "  Lehrbuch  " 
and  give  the  years  of  first  publication  as  1830  and  1845. 

Becker  (p.  71)  mentions  "  four  nearly  coincident  experi- 
ments" published  in  Poggendorff's  Annalen  for  1826,  mean- 
ing Pb  =.  207.12  for  O  =  16.  He  also  refers  to  "six 
experiments  "  under  the  heading  207.078,  as  published  in  the 
same  Annalen  in  1830.  As  last  reference  he  says  that 
Berzelius  "  selected  "  five  of  the  preceding  analyses  giving 
207.14  and  gives  as  source  for  this  reference  the  same  volume 
and  page  of  the  Lehrbuch  above  mentioned. 

Turning  to  the  Skandinavian  Sebelien  (p.  145-146)  we 
find  the  identical  nine  determinations  quoted  by  Clarke — 
identified  by  the  weights  given — but  in  a  different  order,  and 


80  ABSOLUTE   ATOMIC   WEIGHT. 

here  referred  to  the  Transactions  of  the  Swedish  Academy 
for  1830. 

In  the  absence  of  the  original  publications  (we  have  only 
the  3rd  edition  of  the  Lehrbuch  and  a  French  translation 
published  in  Brussels,  and  neither  the  Annalen  nor  the 
Handlingar)  we  conclude  that  all  these  determinations  were 
made  at  or  before  1830. 

Both  the  German  and  the  American  authors  (re-calcula- 
tors) are  apparently  in  error  in  making  the  last  (fifth) 
edition  of  the  Lehrbuch  a  date  mark  for  this  great  work  of 
the  Skandinavian  Chemist  Berzelius. 

Evidently,  Berzelius  in  the  last  edition  of  his  great  work, 
merely  summarized  the  result,  by  using  only  five  of  his  nine 
determinations. 

Sebelien  mentions  this  exclusion  of  four  determinations 
of  the  nine,  as  having  been  made  by  Berzelius  because  they 
differed  most  from  the  mean. 

Sebelien  specifies  the  very  ones  excluded,  which  we  find 
all  to  belong  to  the  list  marked  "earlier"  by  Clarke,  and 
forming  the  first  four  of  that  list. 

We  therefore  feel  authorized  to-subdivide  that  "earlier" 
list  as  shown  below. 

The  four  determinations  excluded  by  Berzelius  from  his 
Lehrbuch  are  apparently  the  oldest  determinations,  referred 
to  by  Becker  as  published  in  the  Annalen  in  1826. 

The  other  five  determinations  (not  6  as  Becker  has  it) 
were  published  in  1830,  both  in  the  Handlingar  at  Stock- 
holm, and  in  the  Annalen  at  Berlin. 

None  of  this  work  is  later  than  1830. 

The  impression  made  by  the  German  and  American  Re- 
calculators,  that  some  of  this  work  of  Berzelius  was  as  late 
as  1845  a*  least,  is  surely  an  absolute  error. 

Considering  the  great  importance  of  this  series  of  deter- 
minations made  by  Berzelius,  we  deemed  it  necessary  (and 
just  to  Berzelius)  to  establish  the  date  of  this  work. 

We  are  convinced  that  this  work  will  be  looked  upon  as 
the  finest  and  most  important  quantitative  work  of  the 
Century. 

We  now  give  the  weight  (in  grammes)  of  the  nine  deter- 


LEAD.       BERZELIUS.  8 1 

minations  made  by  Berzelius,  and  published  respectively  in 
1826  and  1830. 

The  weights  are  not  reduced  to  vacuum,  though  Berzelius 
satisfied  himself  of  the  influence  of  as  large  a  charge  as  20 
grammes  of  the  oxide  on  the  loss  in  weight. 

The  high  specific  gravity  of  both  the  lead  and  its  oxide, 
made  the  omission  of  such  reduction  insignificant. 

Berzelius'  Reductions  of  Lead  Oxide. 

Analytical 
Year.  Oxide.  Metal.  Ratio. 

1826  8.045  7-467S  0.92    822 

"  14.183  13'165  o-92  822 

10.8645  10.084  °-92  816 

13.1465  12.2045  °-92  835 

1830  21.9425  20.3695  0.92  831 

"  11-159  IO-359  °-92  831 

6.6155  6.141  0.92  828 

14.487  13.448  0.92  828 

14.626  13-5775  0.92  831 

This  column  of  analytical  ratios,  the  real  expression  of 
the  experimental  work  done,  is  certainly  marvelous. 

The  mean  of  the  four  oldest  determinations  is  0.92  824, 
with  a  range  of  19  in  the  5th  place,  in  1826. 

The  mean  of  the  five  later  determinations  is  0.92  830, 
with  a  range  of  3  only — in  1830. 

The  mean  of  all  determinations  made  over  seventy  years 
ago,  is  0.92  827. 

Now  let  us  see  what  the  atomic  ratio  for  this  process  is. 

Pb  :  Pb  O  •=.  207  :  223  =  0.92  825.     Change  3  high. 

This  atomic  ratio  is  practically  identical  with  the  analyt- 
ical ratios  found  by  Berzelius  in  and  before  1830. 

The  mean  of  the  determinations  of  1826  is  one  low  in  the 
5th  place. 

The  mean  of  the  determinations  of  1830  i&five  high  in  the 
5th  place. 

The  mean  of  all  determinations  is  two  high  in  the  5th 
place. 


$2  ABSOLUTE   ATOMIC   WEIGHT. 

The  individual  deviations  of  the  analytical  from  the 
atomic  ratio  are,  in  the  order  stated  : 

1826:     3  low;  3  low;  9  low;   10  high. 

1830:     6  high;  3  high;  3  high;  6  high;  2  high. 

The  earlier  determinations  fall  almost  equally  on  both 
sides  of  the  atomic  ratio. 

The  later  determinations  are  all  high:  2  high,  once;  3 
high,  twice;  6  high,  twice. 

Take  the  entire  series,  and  the  individual  values  of  the 
analytical  ratios  are  identical  in  the  first  three  decimals, 
while  the  last  two  are,  in  the  order  of  magnitude 

16,  once;  22,  twice;  28,  twice;  31,  thrice;  35,  once. 

They  are  properly  distributed  about  the  mean  value  (27) 
to  allow  the  calculation  of  the  probable  error  of  the  mean. 

This  probable  error  is  1.4  in  the  5th  place. 

Surely,  the  atomic  ratio  is  established  as  the  true  ratio  by 
these  analytical  ratios. 

These  determinations  of  Berzelius  leave  no  possible  room 
for  the  supposition  that  the  deviation  of  the  atomic  weight 
of  lead  from  the  standard  207  is  anything  but  zero. 

Hence,  these  determinations  of  Berzelius  demonstrate 
that  the  true  atomic  weight  of  lead  is  207  exactly. 

But  why  has  this  fact  not  been  recognized,  since  these 
experimental  determinations  of  Berzelius  have  been  known 
for  three  quarters  of  a  century? 

Very  simply,  because  chemists,  even  Berzelius  himself 
not  excepted,  took  each  individual  determination  and  from 
it  calculated  the  atomic  weight  of  lead— far  beyond  the 
degree  of  precision  warranted. 

It  is  well  known  that  even  Berzelius  himself  carried  these 
calculations,  for  his  large  unit  of  oxygen  •=.  100,  to  two  or 
three  decimals. 

For  lead  207  this  gives  1293.75  in  Berzelius'  units. 

His  own  calculations,  as  reported  by  Sebelien  (p.  146) 
from  these  determinations  ran  from  1292.000  to  1294.946,  a 
range  of  2.946. 

Now  Berzelius  must  have  had  frequent  occasions  to  notice 


LEAD.       BERZELIUS.  83 


that  what  seems  perfect  and  finely  finished  to  the  naked  eye, 
need  only  be  looked  at  through  a  magnifier — and  it  will  appear 
to  be  rough  and  coarse. 

The  edge  of  a  razor  is  very  fine — but  under  a  microscope 
it  looks  like  a  worn  out  saw. 

Berzelius  unwittingly  magnified  his  errors — and  then  felt 
like  counting  out  some  of  them. 

The  great  chemist  was  a  good  calculator,  and  liked  to 
obtain  six  or  seven  digits  in  his  final  result.  Possibly  he 
used  "  seven  place  logarithms."  See  pp.  44-45. 

The  great  chemist  was  not  of  a  mathematical  turn  of 
mind — not  any  more  than  his  very  noted  re-calculators. 

But  while  he  was  unable  to  stop  at  the  right  time  at  the 
proper  place  in  the  string  of  decimals,  he  knew  all  about  the 
chemical  work. 

While  he  was  as  reckless  in  carrying  the  calculation  of 
additional  decimals  beyond  the  limit  of  his  own  chemical 
determination  as  any  of  the  modern  chemists,  the  re-calcu- 
lators included,  his  fine  chemical  sense,  if  we  so  may  call  it, 
did  not  permit  him  to  introduce  wilfully  corrections  less  in 
amount  than  the  uncertainty  of  his  real  chemical  work. 

It  was,  I  believe,  in  reference  to  this  investigation  that 
Berzelius  made  the  statement  about  the  chemists  who 
strained  at  a  gnat  while  swallowing  camels.  (Sebelien,  p. 
45;  Matthew  XXIII,  24). 

Sebelien  (p.  45)  positively  asserts,  that  Berzelius  never 
reduced  his  weighings  to  vacuum,  because  u  he  had  found 
t{  that  the  single  determinations  deviated  to  a  much  greater 
**  extent  than  the  amount  of  such  correction." 

This  is  just  so  to-day;  but  we  like  to  pretend  to  be  exact, 
we  create  the  show  of  a  high  degree  of  accuracy — and  do  not, 
all  of  us,  realize  how  far  we  modern  chemists  with  balances 
permitting  us  to  "  oscillate  "  to  the  hundredth  or  less  of  a 
milligramme  are  away  off  in  the  woods. 

I  trust  that  this  little  book  will  make  chemists  again  go  to 
the  Grand  Old  Swede  to  learn  how  to  work  to  the  advantage 
of  truth. 


84  ABSOLUTE   ATOMIC   WEIGHT. 

E.    How  I  Learnt  the  Name  Berzelius. 

Early  in  the  summer  of  1853  I  came  to  Copenhagen.  I 
had  never  been  away  from  home ;  my  health  would  not  have 
permitted,  if  means  had  allowed. 

I  had  just  passed  my  examinations  for  admission  in  the 
halls  of  the  university,  together  with  many  other  young 
men,  who  had  enjoyed  the  advantages  of  higher  schools  for 
many  years.  I  had  for  one  year  been  the  happy  possessor 
of  a  couple  of  Danish  works  on  Elementary  Mathematics 
and  a  Danish  grammar  and  a  dictionary — to  learn  both  the 
language  and  the  science — without  a  master. 

After  Professor Ramus  had  examined  me  in  mathematics, 
one  of  the  older  hands  whispered  to  me:  "you  did  very 
well."  I  asked,  "how  can  you  tell  ?"  when  he  called  my 
attention  to  the  significant  fact,  that  the  Professor  had  kept 
one  of  his  boots  on,  entirely  undisturbed,  and  got  the  other 
one  much  less  than  half  off.  This  was  a  sure  sign  of  "  very 
good." 

Professor  Ramus  was  a  most  excellent  teacher  of  mathe- 
matics; I  enjoyed  his  lectures,  though  his  free  use  of  the 
sponge  in  the  left  and  the  chalk  in  the  right  hand  was 
greatly  bewildering  to  the  bulk  of  the  class  in  the  reduction 
and  transformation  of  formulae.  I  was  just  enraptured. 

During  the  summer  the  scourge  of  cholera  developed  in 
Copenhagen,  finding  several  victims  in  the  families  I  was 
staying  with. 

One  day,  in  June,  I  was  invited  to  take  dinner  at  the 
home  of  the  director  of  the  Polytechnic  School,  Professor 
Forchhammer,  in  the  University  Building  on  Norregade  and 
facing  the  Petrikirke. 

During  the  dinner,  a  magnificent  portrait  on  the  wall 
back  of  the  Professor  and  to  my  right  hand,  attracted  my 
very  special  attention,  so  as  to  finally  lead  me  to  inquire 
whom  it  represented. 

Almost  reverentially  Professor  Forchhammer  answered : 
"  That  is  a  portrait  of  the  greatest  chemist  of  the  world,  of 
"  Berzelius." 


LEAD.       BERZELIUS.  85 


To  me,  Forchhammer  represented  the  highest  type  of 
man,  as  to  position  and  learning;  his  naming  Berzelius  in 
that  way,  convinced  me  that  he  was  naming  one  of  the 
greatest  of  earth. 

After  half  a  century  spent  in  the  study  of  chemistry,  I 
have  more  and  more  realized  the  truth  of  the  words  of  my 
teacher  of  chemistry. 

F.    Other  Processes. 

We  have  considered  with  a  reasonable  degree  of  detail 
the  ignition  of  the  carbonate,  the  production  of  the  oxide 
(wet  way)  and  especially  the  reduction  of  the  oxide  in  the 
dry  way,  all  effected  by  Berzelius. 

This  was  done,  first  to  become  acquainted  with  this  new 
kind  of  work,  and  second,  because  the  record  of  the  great 
experimental  labors  of  Berzelius  forms  the  basis  of  our  pres- 
ent investigation,  and  in  truth  of  all  serious  work  on  atomic 
weights. 

While  it  would  be  most  interesting  as  well  as  highly 
instructive,  to  continue  our  exposition  of  the  experimental 
data  with  the  same  amount  of  detail,  space  will  not  allow  us 
to  do  so. 

Besides,  we  can  now  readily  comprehend  the  data  in  a 
compressed,  tabular  form,  followed  by  a  brief  mention  of 
the  most  important  points  involved. 

In  a  subsequent  part  of  this  book,  all  the  researches 
made  will  be  given  with  a  sufficient  and  uniform  fullness  of 
detail. 

Referring  to  that  part  of  this  book  for  such  details,  we 
here  shall  give  only  the  final  results  of  all  the  researches 
made  on  the  atomic  weight  of  lead  by  Berzelius  and  other 
chemists. 

In  the  table  now  following  we  have  stated  all  the  eleven 
chemical  processes  that  have  been  used  for  the  determination 
of  this  atomic  weight,  reserving  to  each  one  a  single  line. 

For  each  one  of  these  chemical  reactions  we  give  first 
the  chemical  formula  of  the  two  substances  weighed,  one  of 
which  has  been  converted  into  the  other;  second,  we  give 


86 


ABSOLUTE   ATOMIC    WEIGHT. 


the  standard  atomic  weight  of  each  of  these  compounds  by 
summing  the  standard  atomic  weights  of  the  symbols  speci- 
fied in  the  formula;  third,  we  give  the  atomic  ratio  by  divid- 
ing the  second  into  the  first,  carrying  out  this  division 
uniformly  to  five  decimals.  Lastly  we  add  the  change  which 
this  ratio  undergoes  if  we  raise  the  atomic  weight  of  lead  to 
207.1. 

The  reason  why  we  carry  out  the  division  to  Jive  places 
has  already  been  stated,  but  may  be  repeated  here.  By  an 
extended  critical  examination  of  all  the  atomic  weight  deter- 
minations we  have  found  this  number  of  decimals  practi- 
cally the  limit  of  accuracy  or  precision  attained. 

The  unit  in  the  last  or  Jifth  place  represents  the  one 
hundred  thousandth  part,  by  weight,  of  the  amount  of  sub- 
stance operated  upon.  This  is  the  limit  of  precision 
attained  in  the  best  work. 


Atomic  Ratios  for  Reactions  Used. 


1.  PbO 

2.  Pb 

3.  PbO 

4.  PbChS 
5-  PbO 

6.  PbO4S 

7.  Pb(OsN)2 

8.  PbCh 

9.  Pb(OaN)2 

10.  PbCh 

11.  2AgCl 


PbOsC 

PbO 

Pb 

PbO 

Pb(O3N): 

Pb 

Pb 

Pb 

Pb04S 
2Ag 

PbCh 


Change. 

223 

267=0.83 

521 

6 

high. 

207 

223 

=  0.92 

825 

3 

high. 

227 

207 

:= 

I 

.07 

73° 

6 

high. 

303 

*   tj 

== 

i 

•35 

874 

1  6 

low. 

223 

33  1 

zr 

0 

.67 

37i 

1  1 

low. 

303 

207 

= 

I 

.46 

377 

23 

low. 

331 

207 

^z 

I 

•59 

903 

29 

low. 

278 

207 

—  • 

I 

•34 

300 

17 

low. 

331 

303 

m 

I 

.09 

241 

3 

low. 

278 

216 

= 

I 

.28 

703 

*7 

high. 

287 

278 

~ 

I 

•03 

237 

37 

low. 

The  change  is  the  number  of  units  in  fifth  place  changed 
in  the  direction  stated  by  raising  the  atomic  weight  o.i  or 
207.1. 

The  first  three  reactions  here  tabulated  have  been  fully 
considered  in  preceding  sections. 

The  fourth  reaction  represents  the  synthesis  of  lead  sul- 
phate from  the  oxide  and  sulphuric  acid,  driving  off  the 
excess  of  acid  by  heat.  It  is  evidently  a  reaction  that  cannot 
admit  of  a  high  degree  of  precision. 


LEAD.       BERZELIUS.  87 

Only  Turner  has,  in  1833,  made  determinations  of  this 
kind,  7  in  number;  range  210;  mean  70  high. 

The  range  being  three  times  the  extent  of  the  deviation 
of  the  mean  from  the  atomic  ratio,  this  process  is  thereby 
proved  unfit  for  accurate  atomic  weight  determination. 

It  would  surely  be  scientifically  incorrect  to  ascribe  the 
deviation  to  the  atomic  weight,  while  it  is  evidently  due  to 
the  lack  of  precision  of  the  reaction  itself. 

The  change  of  "  16  low"  for  a  rise  o.i  in  the  atomic 
weight  of  lead  would  indicate  the  atomic  weight  206.6,  if  the 
process  could  be  used  for  such  determination. 

The  fifth  reaction  represents  the  process  of  ignition  of 
the  nitrate.  It  was  carried  out  4  times  by  Anderson  in 
Svanberg's  laboratory.  Range  n,  mean  32  high. 

This  would  require  Pb  =  206.7  ^  the  process  were 
reliable. 

The  sixth  reaction  represents  the  production  of  the  sul- 
phate from  the  metal  and  the  acid. 

Berzelius  made  4  determinations.  Range  78,  mean  42 
high. 

Turner,  1833,  made  3  determinations.  Range  55,  mean 
24  high. 

While  in  these  two  series  of  determinations  we  notice  an 
approach  to  the  atomic  ratio,  the  range  is  diminishing,  we 
notice  in  the  later  determinations  by  Stas,  6  in  number,  a 
diminution  of  the  range  to  24  with  an  increase  of  the  devi- 
ation to  51  high,  corresponding  to  Pb  =:  206.8. 

But  at  the  same  time  a  mere  inspection  of  the  individual 
analytical  ratios  shows  that  they  systematically  change  with 
the  amount  of  lead  operated  upon. 

Figure  2  on  Plate  I,  facing  page  31  of  our  True  Atomic 
Weights,  1894,  shows  this  fact  plainly  to  the  eye.  We  may 
also  refer  to  the  figure  given  by  us,  page  432,  T.  116,  of  the 
Comptes  Rendus  for  1893. 

There  is  absolutely  no  possibility  of  denying  the  fact, 
that  the  work  of  Stas  gives  analytical  ratios  systematically 
varying  with  the  amount  of  lead  used. 

This  fact  excludes  these  determinations  as  chemically 
unfit. 


88  ABSOLUTE   ATOMIC   WEIGHT. 

The  se-^cnth  reaction  represents  the  so-called  synthesis  of 
lead  nitrate  from  the  metal  and  the  acid.  Only  Stas  has 
carried  out  this  operation. 

His  series  A  comprises  6  determinations.  Range  14, 
mean  71  high. 

His  later  series  B  comprises  4  determinations.  Range 
u,  mean  67  high. 

Also  these  analytical  ratios  are  not  nearly  constant  with 
non-systematic,  irregular  differences,  but  they  show  system- 
atic variations  with  the  amount  of  lead  used. 

These  systematic  variations  are  even  more  marked  than 
those  shown  by  the  sulphate.  In  the  places  just  cited 
diagrams  drawn  to  scale  present  this  fact  to  the  eye. 

It  is  absolutely  impossible  to  make  use  of  any  such  work 
for  atomic  weight  determination,  because  it  does  not  even 
comply  with  the  condition  insisted  upon  in  all  good  analyt- 
ical work.  See  pp.  53-54. 

It  is  in  no  sense  our  business  to  show  how  Stas  came  to 
make  such  a  mess  of  this  work  that  has  been  so  much 
admired  until  we  showed  this  fatal  error  which  totally  and 
for  ever  must  exclude  this  work  of  his  from  consideration. 

We  tried,  in  our  True  Atomic  Weights,  to  point  out  the 
reason.  But  it  seems  not  yet  to  have  been  understood  by 
the  admirers  and  imitators  of  the  work  of  Stas. 

In  this  place  we  state  once  more,  that  this  work  of  Stas, 
bearing  on  its  face  the  plain  systematic  error  (whatever  its 
cause  may  be)  is  by  this  simple  fact  necessarily  excluded 
from  consideration  in  the  determination  of  the  atomic 
weight  of  lead  by  every  chemist  who  understands  that  the 
amount  of  nitrate  per  gramme  of  metal  must  not  system- 
atically vary  with  the  amount  of  metal  employed. 

If  any  individual,  claiming  to  be  a  chemist,  or  even 
holding  a  professorship  in  chemistry  and  receiving  a  salary 
as  such  from  a  state  or  an  institution,  fails  to  understand 
this  fact  here  stated  and  shown  to  exist  in  the  record  of  Stas 
himself,  such  individual  eo  ipso  is  not  a  chemist,  is  unfit  for 
such  a  professorship  and  draws  the  salary  as  an  impostor. 

If  he  be  an  editor  of  Chemical  News,  he  is  blocking  the 


LEAD.       BERZKLIUS.  89 


wav  of  chemistry,  and  defrauding  his  subscribers,  as  is 
Mr.  Wm.  Crookes,  Chemical  News,  vol.  73,  p.  231 ;  1896. 

The  eighth  reaction  represents  the  synthesis  of  lead 
chloride  in  the  dry  way  from  the  elements.  The  reaction 
cannot  give  reliable  results  for  many  reasons.  The  determ- 
inations made  must  necessarily  be  without  value. 

Marignac  is  the  only  chemist  who  has  used  this  process. 
In  1846  he  made  3  determinations.  The  range  was  moderate, 
35 ;  but  the  mean  is  109  low.  This  would  require  Pb  =  207.6 
at  least,  as  the  change  pero.i  is  17  low. 

This  is  not  only  absolutely  inconsistent  with  the  determ- 
inations of  Berzelius,  but  conflicts  also  with  the  u  demands  " 
of  the  sulphate  and  nitrate,  which  would  require  an  atomic 
weight  considerably  below  207. 

The  only  thing  to  be  done  is  to  throw  out  and  disregard 
faulty  processes. 

Our  chemical  record  of  atomic  weight  determinations 
should  cease  to  be  a  stinking  olla  podrida,  filled  by  the  use  of 
bad  analytical  methods. 

The  ninth  reaction  represents  the  change  of  nitrate, 
effected  by  heating  it  carefully  with  an  excess  of  sulphuric 
acid. 

This  is  a  very  questionable  operation  for  atomic  weight 
determination.  Only  Turner,  in  1833,  tried  it  three  times. 
The  range  was  small,  12;  the  mean  was  66  high. 

By  our  table  we  see  that  this  would  require  the  atomic 
weight  of  lead  to  be  taken  at  204.8. 

It  is  preposterous  to  consider  such  a  result  seriously. 

The  tenth  reaction  is  the  unreliable  silver  process  in  the 
wet  way. 

Marignac,  in  1858,  made  4  determinations  with  a  range  of 
101  the  mean  was  18  high.  Dumas,  in  1860,  gave  a  mean  47 
high. 

These  results  would  again  raise  the  atomic  weight, 
Marignac  about  to  207.1,  Dumas  to  207.3. 

A  blunderbuss  is  a  rather  poor  thing  to  use  where  a  good 
rifle  is  required. 

The  eleventh  reaction  is  much  worse,  since  it  involves  the 
use  of  silver  chloride  in  the  wet  way. 


9O  ABSOLUTE   ATOMIC   WEIGHT. 


Marignac  made  3  determinations  in  1846.  The  range  was 
enormous,  380;  the  mean  27  low. 

This  mean  would  raise  the  atomic  weight  to  207.1  only; 
but  the  mean  of  such  a  series  has  absolutely  no  value.  The 
range  is  too  dangerous  for  the  bystanders. 

G.    What  Shall  be  Done  with  Faulty  Methods  and  False  Results? 

In  conclusion  we  find  that  the  first  three  reactions,  in  the 
hands  of  Berzelius,  gave  perfectly  concordant  results,  exactly 
conform  to  the  standard  atomic  weight,  which  thus  was 
experimentally  demonstrated  to  be  the  true  atomic  weight  of 
lead.  These  are  the  best  and  sharpest  reactions,  especially 
the  third. 

All  the  other  reactions  are  unfit  for  atomic  weight  deter- 
minations and  give  conflicting  results. 

The  ninth  reaction  would  run  down  the  atomic  weight  of 
lead  to  204.8  while  the  eighth  would  run  it  up  to  207.6. 

This  range  of  2.8  in  the  resulting  atomic  weight  is  per- 
fectly preposterous;  it  does  not  leave  the  real  atomic  weight 
in  the  slightest  doubt,  but  merely  confirms  the  opinion 
formed  theoretically  from  the  chemical  character  of  the 
reaction,  that  it  is  unfit  for  the  purpose. 

In  each  one  of  these  cases  we  have  given  striking  facts 
showing  that  the  reaction  is  unfit  for  atomic  weight  deter- 
mination, either  by  excessive  range  of  the  results,  by  syste- 
matic variation  with  the  amount  of  substance  used,  or  for 
other  reasons. 

Now,  what  do  good  and  honest  chemists  do  when  a  reac- 
tion is  proposed  for  ordinary  quantitative  chemica1  analysis? 

Do  they  not  first  test  it  upon  materials  of  known  compo- 
sition? and  if  it  fails  to  give  correct  results,  do  they  use  the 
process  when  they  have  an  analysis  to  make  for  any  body? 
Do  our  treatises  continue  to  give  details  about  such  pro- 
cesses, or  do  they  at  most  mention  and  condemn  them  as 
unfit  for  use? 

And  why  should  any  chemist  act  differently  towards  pro- 
cesses proposed  to  be  used  for  the  highest  problem  of  the 
science? 


IRON.       SVANBERG.  9! 


If  any  process  or  reaction  is  proposed  for  atomic  weight 
determination,  and  upon  trial  has  given  absurd  results  in 
conflict  with  rational  and  exact  methods,  or  if  it  gives  results 
which  in  themselves  by  an  excessive  range  or  by  systematic 
variations  or  in  any  other  way  show  the  process  to  be  unfit 
for  such  a  purpose,  is  not  the  only  thing  left  to  be  done,  the 
exclusion  of  the  same,  and  of  its  results,  from  the  body  of 
the  science — with  a  simple  note  of  the  fact? 

To  suppose  for  a  moment  that  by  any  hocus-pocus  of  a 
mathematical  or  enigmatical  character  any  person  can  throw 
notoriously  false  results  obtained  by  irrational  process, 
together  with  such  condemned  by  their  own  originators  as 
false  and  worthless,  into  a  pot  or  mill  and  turn  some 
mechanical  crank  and  draw  out  true  and  reliable  results — is 
giving  an  exhibition  of  the  worst  possible  characters  of  a 
a  scientific  crank. 

The  mere  fact  that  such  a  scientific  crank  is  the  Chief 
Chemist  of  the  U.  S.  Department  of  the  Interior  has  no 
bearing  on  the  chemical  question  involved. 

And  to  offer  to  the  scientific  public  a  collection  of  false 
methods  and  false  data  obtained  thereby  in  the  garb  of  truth 
and  in  the  form  of  scientific  language  and  formula,  is  a 
crime  against  nature  and  against  scientific  morals. 

And  the  institution  founded  for  the  increase  and  diffusion 
of  knowledge  among  men  per  orbem,  that  would  print,  pub- 
lish and  disseminate  such  rotten  abominations  needs  first  of 
all  a  thorough  driving  out  of  the  guilty,  followed  by  a  most 
thorough  disinfection  and  renewal  of  the  entire  institution. 


III.    THE  ATOMIC  WEIGHT  OF  IRON.     SVANBERG. 

The  determination  of  the  true  atomic  weight  of  iron  we 
also  owe  to  Berzelius  and  his  school. 

With  that  true  insight  into  the  conditions  of  quantitative 
accuracy  of  chemical  processes,  Berzelius  already  in  1809, 
had  selected  the  very  best  process  possible  for  iron,  namely, 
the  change  of  the  metal  into  its  sesquioxide  and  the  reduc- 
tion of  the  latter. 


ABSOLUTE   ATOMIC   WEIGHT. 


In  his  Annual  Report  presented  to  the  Swedish  Academy 
of  Sciences  on  the  last  of  March,  1844,  he  gives  an  interesting 
summary  of  the  work  done  by  him  and  his  school  up  to  that 
time,  including  the  final  work  of  Svanberg. 

I  possess  only  the  8  volumes  of  these  famous  yearly 
reports  of  Berzelius,  translated  by  Plantamour.  The  above 
historic  sketch  is  found  on  pages  64  to  67  of  the  5th  volume 
of  this  French  series,  corresponding  to  the  24th  volume  of 
the  German  edition. 

The  earliest  determination  of  Berzelius  dates  back  to 
1809,  when  he  found  69.34  per  cent  of  iron  in  ferric  oxide  by 
preparing  ferric  oxide  from  purest  iron  nails,  in  which  he 
had  determined  the  trace  of  carbon. 

He  admits,  in  this  report,  that  at  the  time  he  could  not 
suspect  the  effect  of  a  small  amount  of  silicon  present  in  that 
iron. 

Magnus — of  the  school  of  Berzelius— confirmed  this 
result  by  reduction  of  this  oxide  in  a  current  of  hydrogen. 
He  obtained  69.329  per  cent  of  iron. 

Stromeyer,  the  discoverer  of  the  metal  cadmium,  showed 
that  these  results  were  considerably  too  low;  but  his  value 
69.85  found  no  immediate  acceptance. 

Hence  Stromeyer,  in  1843,  caused  the  work  to  be  care- 
fully extended  in  his  laboratory  by  Wackenroder  who  found, 
in  five  determinations,  from  69.62  to  69.99  Per  cent  °f  iron 
by  reduction  in  a  current  of  hydrogen.  See  also  Sebelien, 
p*  184. 

These  determinations  running  up  to  within  one  hun- 
dredth of  one  per  cent  to  the  full  seventy  (which  we  here 
shall  find  to  be  the  true  value),  influenced  Berzelius  to 
resume  the  work. 

He  induced  Lars  F.  Svanberg  to  undertake  a  fundamen- 
tal revision  of  the  atomic  weight  of  iron  in  his  laboratory. 
This  was  done  with  the  assistance  of  Norlin  and  "  proved 
"  that  the  results  of  Stromeyer  came  nearer  the  truth  than 
{c  had  been  supposed." 

Svanberg-  and  Norlin,  in  the  laboratory  of  Berzelius, 
and  under  his  direction  and  with  his  assistance,  produced  a 
work  that  is  worthy  of  the  master  himself. 


IRON.       SVAXBERG.  93 


We  would  like  to  enter  upon  some  of  the  more  interest- 
ing chemical  points,  but  space  forbids.  We  shall  have  to 
confine  ourselves  to  the  systematic  statement  of  the  results 
obtained,  using  the  form  already  familiar  to  the  reader. 

The  results  obtained  by  other  chemists  will  also  be  stated 
in  the  same  form.  Erdmann  and  Marchand  are  thorough 
representatives  of  the  method  of  Berzelius. 

Fe2  :  Fe2  Oa  =r  112  :  160^1:0.70  ooo.     Change  19  high. 

Berzelius,  1809, Mean  66  low. 

Magnus,  .     ,    .    ,     .    . :  .     •    •     •        "      68  low. 

Stromeyer,  1826,  .  V  .  .  -.".'...  "  15  low. 
Wackenroder,  1843,  <  .  .  Results  from  38  to  i  low. 
Svanberg  and  Norlin,  1844: 

Oxidation,       7  Det.,  977  —  928;     49.     Mean  47  low. 

Reduction,      7  Det.,  072 —014;     58.         "       35  high. 

Mean,  14  Det.,  072 — 928;  144.         "        6  low. 

Erdmann  and  Marchand,  1844.     Reduction  only: 

Substance  A,  5  Det.,  030  —  962;     68.     Mean    Slow. 

Substance  B,  3  Det.,  055  —  015;     40.        "       38  high. 

Mean,  8  Det., "         9  high. 

Berzelius,    1844,        2  Det.,  022  —  018;       4.         "       20  high. 
Maumene",  1850,        6  Det.,  oio  —  990;     20.         ff         i  high. 
The  last  two  series  were  made  by  wet  way  synthesis — 
dissolving  pure  iron  in  nitric  acid  with  final  ignition. 

We  notice  that  the  earlier  determinations  were  low. 
Berzelius  over  60  low  in  1809,  Stromeyer  only  15  low  in  1826, 
while  Wackenroder  in  1843,  almost  reached  the  standard  as 
a  limit. 

The  most  complete  work  of  Svanberg  and  Norlin  gave 
constantly  low  results  by  oxidation,  high  results  '.  y  reduc- 
tion; indicating  minute  constant  errors  acting  in  opposite 
directions,  and  giving  the  more  reliable  mean  only  6  low. 
This  makes  their  mean  doubly  valuable,  according  to  the  old 
rule  of  Berzelius. — Sebelien  p.  13;  True  Atomic  Weights  p. 
16 — p.  3,  Supra. 

The  determinations  of  Erdmann  and  Marchand  were  all 
made  by  reduction  only,  but  the  substance  operated  upon 
was  obtained  from  ferrous  oxalate  prepared  in  two  different 
ways. 


94  ABSOLUTE   ATOMIC   WEIGHT. 

In  their  results  we  have  quite  an  indication  of  the  effect 
of  the  manner  of  preparation  of  apparently  the  same  oxide. 
The  mean  of  all  is  only  9  high. 

Berzelius  himself  (1.  c.)  accepts  the  results  of  Svanberg 
and  Norlin  with  the  distinct  statement  that  his  own  deter- 
minations last  given  are  not  to  be  considered. 

The  final  mean  of  the  determinations  of  Svanberg  and 
Norlin  would  lower  the  atomic  weight  about  0.03. 

The  mean  of  Erdmann  and  Marchand  would  raise  it 
about  0.05. 

But  both  combined  would  give  a  final  mean  %  low,  which 
would  lower  the  atomic  weight  only  0.002. 

Evidently,  all  such  calculations  are  based  upon  assuming 
an  accuracy  of  the  mean  higher  than  the  facts  substantiate. 

All  we  can  conclude  is  that  the  determinations  made  do 
not  establish  any  deviation  from  the  standard  value  56. 

Therefore,  the  only  statement  that  expresses  the  actual 
experimental  determinations  made  is  that  the  true  atomic 
weight  of  iron  is  56  exactly,  no  positive  evidence  having 
been  obtained  to  establish  any  deviation  however  slight, 
from  this  standard  number,  not  even  to  the  extent  of  one 
thousandth  of  a  ttnit. 

Before  closing  this  subject  we  may  mention  the  deter- 
minations by  Richards  and  Baxter,  recently  made  by  reduc- 
tion with  electrolytic  hydrogen. 

The  ferric  oxide  was,  for  the  first  series,  obtained  by 
calcining  the  hydrate;  for  the  second  series  by  ignition  of 
the  nitrate.  The  results  are  : 

Richards  and  Baxter,  1900*  : 

Series    I,  2  Det.,  968  —  955;   13  Mean,  39  low. 

"       11,5      "    959  —  95i;    §      "      44  low. 

Mean         7      "    968  —  951517       "      42  low. 

The  weighings  are,  of  course,  stated  to  the  hundredth  of 
the  milligramme. 

I  do  not  see  that  these  new  determinations  add  anything 
to  the  stock  of  our  knowledge. 

They  do  not  conflict  with  the  reductions  of  Svanberg 
(mean  35  high)  or  Erdmann  (B,  38  high). 

*  Report  Chemical  News,  1901,  April  4;  vol.  83,  pp.  161   162. 


MERCURY.       ERDMAXN.  95 

Hence,  the  conclusion  above  stated,  remains  the  true 
statement  of  all  the  actual  experimental  determinations. 

The  only  additional  point  established  is  this,  that  the 
pretended  weighing  to  the  hundredth  of  a  milligramme  did 
not  add  the  least  to  the  accuracy  of  the  results  obtained  half 
a  century  ago  by  weighing  to  the  milligramme  only. 

The  final  value  Fe  55.89,  given  by  these  recent  authors 
as  based  upon  their  new  data,  must  be  thrown  into  the 
waste  basket  with  all  the  other  fancied  values  of  that  kind. 

In  conclusion  we  merely  mention  the  few  useless  deter- 
minations by  Dumas  in  1860,  using  ferrous  and  ferric  chloride 
against  silver. 

In  our  complete  alphabetical  summary  it  will  be  seen 
that  the  means  are  70  and  90  high,  with  a  range  of  158  and 
39  in  ferrous  and  ferric  chloride  respectively. 

IV.     THE  ATOMIC  WEIGHT  OF  MERCURY.     ERDMANN. 

The  two  German  Chemists,  Otto  Linne  Erdmann  and 
Richard  Felix  Marchand  have  done  most  excellent  chemical 
work  in  atomic  weight  determination,  in  perfect  accord  with 
the  practice  of  the  School  of  Berzelius. 

They  have,  together,  made  determinations  upon  which 
we  base  the  absolute  atomic  weights  of  mercury  and  of 
sulphur.  To  avoid  double  names,  we  ascribe  Hg  to  Erdmann 
and  S  to  Marchand. 

They  made,  in  1844,  five  admirable  distillations  of  mercury 
from  its  oxide  in  a  current  of  carbonic  acid  gas. 

Having  referred  to  necessary  details  of  this  admirable 
chemical  work  before,  pp.  61-63,  we  need  here  give  the 
weighings  (reduced  to  vacuum)  and  analytical  ratios  only: 

Xo.  Oxide.  Metal.  Analyt.  Ratio. 

1  82.0079  75-9347  0.92  594 

2  51.0320  47-2538  0.92  597 

3  84.4996  78.2501  0.92  604 

4  44-6283  4T-3285  0.92  606 

5  118.4066  109.6408  0.92  597 
Grammes.                                            Mean  0.92   600 
Hg  :  Hg  O  =  200  :  216  =  0.92  593.    Chg.  3  high. 


96  SULPHUR.        MARCHAND. 

The  chemical  process  here  expressed  in  standard  atomic 
weights  gives  the  atomic  ratio  stated. 

The  individual  determinations  are  all  high,  but  in  the 
order  of  record  only  i,  4,  u,  13,  4  high  in  fifth  place. 

The  mean  is  only  7  high;  the  range  only  i2_,  the  extremes 
being  606  —  594. 

As  the  range  12  includes  the  deviation  7,  the  data  of  the 
experiments  do  not  allow  to  depend  upon  this  mean  deviation. 
Furthermore,  while  the  individual  deviations  are  all  high, 
the  smallest  brings  the  result  to  -within  a  single  unit  in  the 
fifth  place. 

The  experimental  data  do  not  establish  any  deviation 
from  the  standard  atomic  weight  200,  which  therefore  is  the 
true  atomic  weight  of  mercury. 

If  we  were  to  follow  the  erroneous  process  of  calculating 
atomic  weights  to  decimals  not  determined  by  the  precision 
of  the  experiments,  the  mean  would  give  us  200.2;  but  the 
range  12  corresponds  to  an  uncertainty  of  0.4,  and  thus 
shows  the  fallacy  of  such  calculation. 

V.     THE  ATOMIC  WEIGHT  OF  SULPHUR.     MARCHAND. 

Erdmann  and  Marchand  also  distilled  mercury  from  pure 
mercuric  sulphide  mixed  with  copper.  The  following  are 
the  weights  and  the  analytical  ratios  t 


STo.                 Sulphide. 

Metal.                  Analyt.  Ratio. 

I                   34'3568 

29.6207               0.86  215 

2                   24.8278 

21.40295             0.86  206 

3              37-2177 

32.08416             0.86  207 

4               80.7641 

69.6372               0.86  223 

Grammes. 

Mean  0.86  213 

Hg  :  Hg  S  =  200  : 

232  =  0.86  207.    Chg.  7  high. 

The  chemical  process  here  expressed  in  standard  atomic 
weights  gives  the  atomic  ratio  stated.  For  one  tenth  added 
to  the  200  of  mercury,  the  atomic  ratio  would  rise  7  or  be 
7  high. 

The  mean  analytical  ratio  is  only  6  high.  The  extremes 
are  223  —  206,  giving  a  range  of  17. 


CHLORINE.      TURNER.  97 

The  individual  deviations  of  the  analytical  ratios  from 
the  atomic  ratio  are,  in  the  order  of  the  record,  8  high,  i  low, 
zero,  1 6  high. 

The  middle  two  determinations  are  exactly  coincident 
with  the  calculated  value.  The  first  deviates  to  about  one 
tenth  and  the  last  to  about  two  tenths  of  unit  on  the  atomic 
weight  of  mercury,  raising  the  same. 

But  the  range  or  uncertainty  of  17  (corresponding  to  2^3 
tenths)  is  greater  than  these  deviations 

Accordingly,  we  are  compelled  to  admit  that  the  experi- 
mental determinations  fix  the  true  atomic  weight  of  mercury 
at  the  value  of  its  standard  atomic  weight,  within  the  limit 
of  precision  of  the  determinations  made. 

But  the  work  on  the  oxide  fully  establishes  the  atomic 
weight  of  mercury  as  200.  We  can,  therefore,  use  these 
distillations  of  the  sulphide  for  the  determination  of  the 
atomic  weight  of  sulphur,  precisely  as  originally  intended 
by  these  eminent  chemists. 

To  do  so,  we  need  only  calculate  the  change  in  the  atomic 
ratio  corresponding  to  a  rise  of  o.i  in  the  standard  atomic 
weight  of  sulphur,  namely  32. 

We  find  this  change  (for  S)  37  low.  Now,  the  mean 
analytical  excess  was  found  above  to  be  6  high.  This  is  a 
trifle  less  than  £  of  the  change;  hence  corresponds  to  a 
departure  of  £  of  one  tenth  or  0.017,  direction  low. 

Hence  8  =  31.983. 

We  understand,  of  course,  the  true  signification  of  this 
expression.  It  means  that  the  determinations  of  Erdmann 
and  Marchand  give  a  possible  departure  of  0.02  low  of  the 
true  atomic  weight  of  sulphur  32,  but  that  this  departure  is 
not  established,  rather  simply  marks  the  limit  of  precision. 

VI.    THE  ATOMIC  WEIGHT  OF  CHLORINE.     TURNER. 

The  atomic  weight  of  mercury  having  been  established, 
we  can  next  use  other  mercury  compounds  for  the  determi- 
nation of  other  metalloids. 

Since  mercuric  chloride  can  be  produced  in  purest  crystal 
form,  its  distillation  will  furnish  the  atomic  weight  of 
chlorine. 


98  ABSOLUTE   ATOMIC   WEIGHT. 

Lars  Svanberg   made   three  excellent   distillations   with 
lime  according  to  the  method  of  Erdmann  and  Marchand. 
Hg  :  HgCh  =r  200  :  271  ==0.73  Soi.     Change  48  low. 

Svanberg's  Distillations,  1848. 

No.     Sublimate.     Mercury.        Analyt.  Ratio.        Excess. 

1  12.048          8.889  °'73  7§°  2I    l°w> 

2  12.529        9.2456  794  7  low. 

3  12.6491       9.3363  Sio  9  high. 
Grammes.                  Mean  0.73  795  6  low. 

We  notice,  the  deviations  are  to  both  sides,  very  small, 
except  the  first.  If  this  first  attempt  were  discarded,  the  final 
excess  would  be  i  high  only. 

Taking  all  determinations  as  of  equal  value,  the  mean 
analytical  excess  is  6  low,  which  represents  %  of  the  change 
due  to  o.i,  or  0.012  on  the  atomic  weight,  in  opposite  direc- 
tion, hence  giving  a  positive  departure. 

That  is  35.512  or  say  35.51. 

The  real  meaning  is  that  35.5  is  the  true  atomic  weight, 
with  a.  possible  deviation  indicated  of  o.oi  high,  but  not  fixed, 
as  it  is  within  the  limit  of  precision. 

Millon,  in  1846,  had  made  four  less  accurate  distillations, 
obtaining  a  mean  analytical  ratio  of  0.73  845  which  is  44 

high- 
Turner,  in  1833,  set  free  mercury  by  means  of  stannous 
chloride,  collecting  and  weighing  the  mercury  thus  set  free. 
His  results  are: 

Xo.     Sublimate.     Mercury.        Analyt.  Ratio.        Excess. 

1  60.682       44.782  0.73  798  3  low. 

2  99.06        73-°9  784          17  low. 
Grains.                        Mean  0.73  791  10  low. 

The  work  of  Svanberg  in  1848,  is  considerably  more 
accurate  than  that  of  Turner  in  1833,  as  is  but  natural, 
especially  as  Svanberg  had  the  benefit  of  the  excellent  work 
of  Erdmann  and  Marchand. 

If  Svanberg's  name  were  not  already  associated  with  iron, 
it  would  belong  here  for  chlorine. 


CHLORINE.       TURNER. 


99 


Consequently  the  honor  belongs  to  the  best  chemists  of 
the  earlier  schools;  that  is,  to  Turner,  who  has  done  so 
much  really  good  work  in  this  field. 

We  may  find  this  decision  objected  to,  at  first  sight.  But 
since  Turner  established  the  atomic  weight  of  chlorine 
within  the  limit  of  0.02  while  thirty  years  later  Stas  was  over 
0.05  in  the  wrong  direction,  I  suppose  the  honor  of  Turner 
will  not  be  contested. 

Let  us  see.  The  mean,  10  low,  with  change  48  low,  is 
practically  one-fifth  of  one-tenth,  or  0.02  and  high,  or  Cl  =. 
35.52.  That  is,  as  above  stated,  establishing  the  absolute 
atomic  weight  at  35.5  exactly,  within  0.02  as  the  limit  of 
precision,  preferably  upward. 

Good  Old  Chemists  Abused  by  Clarke. 

In  conclusion  I  have  once  more  to  refer  to  those  "  Con- 
stants of  Nature  "  because,  as  usual,  Clarke  is  shamefully 
unjust  to  our  excellent  pioneer  workers. 

The  very  first  sentence  under  Mercury  (edition  1897,  p. 
1 66)  reads: 

te  In  dealing  with  the  atomic  weight  of  mercury  we  may 
"  reject  the  early  determinations  of  Sefstrom  and  a  large 
"  part  of  the  work  done  by  Turner." 

Sef Strom's  work  dates  from  1812,  and  reaches  to  7.97  for 
oxygen  per  hundred  of  mercury;  that  is  within  0.03  of  [ the 
truth.  It  corresponds  to  01=15.94;  is  therefore  twice  as 
accurate,  as  "  the  latest  fad  of  Clarke,  15.88." 

Turner,  in  two  determinations  of  pure  oxide  (from 
nitrate)  obtained  the  analytical  ratio  0.92  605  which  is  12 
high  only.  His  determination  of  chlorine  is  much  more 
correct  than  that  of  Stas. 

Both  of  these  early  chemists  did  most  admirable  work, 
indeed.  They  deserve  our  highest  respect.  Their  work  is 
more  reliable  than  much  of  the  work  of  to-day. 

The  chief  official  chemist  of  our  National  Government 
ought  not  to  defame  the  great  early  chemists  who  did  excel- 
lent work  in  atomic  weight  determination — a  work  that  he 
has  disgraced. 


IOO  ABSOLUTE   ATOMIC    WEIGHT. 

Hardin's  Electrolyses. 

His  electrolyses  of  mercuric  oxide  have  been  withdrawn. 
See  p.  30,  supra. 

Those  of  silver  and  mercury  compounds  in  the  same  cir- 
cuit, have  also  been  destroyed  by  te selection;"  see  Hardin's 
Thesis,  1896,  pp.  38,  39. 

There  remain  his  electrolyses  of  the  chloride,  bromide 
and  cyanide  of  mercury,  published  in  that  Thesis. 

There  also  remains  an  ugly  suspicion  of  selection,  of 
course.  His  results  are  remarkably  concordant,  and  sup- 
port the  Stasian  values  of  Clarke — which  need  all  support 
they  can  get  from  any  quarter. 

But  surely,  no  one  can  accuse  this  hopeful  young  Stasian 
to  have  "selected"  anything  in  favor  of  our  heterodox 
atomic  weights.  Let  us  therefore,  examine  the  three  series 
he  has  not  withdrawn,  after  publication. 

He  always  weighs  the  substance  and  the  metal.  We  will 
state  his  results  in  three  lines,  giving  our  atomic  ratio  first: 

Atomic  Ratio.  Comp'd.  Analyt.  Results. 

o-55  555          Bromide.          565  —  548;  17.     Mean    o. 
0.73801  Chloride.         838  —  820;   18.     Mean  28  high. 

0-79365          Cyanide.          342  —  337;     5-     Mean  26  low. 

Taking  the  entire  set  of  10  determinations  each  for  these 
three  compounds,  bona  fide,  they  confirm  our  Hgm2oo 
exactly,  in  a  most  remarkable  manner. 

For  while  the  mean  analytical  excess  for  the  bromide  is 
zero,  those  for  the  other  two  compounds  almost  exactly 
balance. 

The  mean  analytical  excess  of  all  thirty  determinations 
is  practically  zero.  Our  standard  atomic  weight  is  also  the 
absolute,  true  atomic  weight,  Hg  =  200  exactly,  according 
to  the  30  experiments  of  Hardin,  if  they  are  bona  fide  deter- 
minations. 

If  so,  we  have  an  interesting  case  of  constant  errors 
determined  by  the  nature  of  the  substance  operated  upon. 
For  the  bromide,  as  might  be  expected,  the  constant  error  is 


CARBON.       DUMAS. 


zero;  for  the  other  two  it  operates  in  opposite  directions, 
balancing  in  amount. 

The  case  of  Hardin  shows  exactly  how  demoralizing  the 
influence  of  the  Chief  Chemist  Clarke  has  been.  Concord- 
ance, minute  "  probable  errors  "  are  insisted  upon  by  this 
High  Muckamuck  of  the  National  Government. 

Hence — the  supply  follows  the  demand;  and  with  it, 
truth  and  science  are  defaced,  and  a  probably  excellent 
young  worker  wrecked. 

How  long  is  this  nation  going  to  allow  our  official  Olla 
Podrida  Cook  to  terrorize  American  students  of  Science  and 
to  disgrace  American  chemistry? 


VII.    THE  ATOMIC  WEIGHT  OF  CARBON.     DUMAS. 

The  great  work  done  by  Dumas  in  perfecting  the  process 
of  the  quantitatively  accurate  combustion  of  the  diamond 
was  strictly  in  line  of  the  school  of  Berzelius,  though 
published  as  an  attack  on  the  Swedish  chemist. 

It  was  soon  followed  by  the  perfection  of  the  process 
devised  by  Berzelius  for  the  determination  of  the  atomic 
weight  of  hydrogen.  In  his  later  years,  Dumas  unfortu- 
nately made  use  of  the  method  of  Pelouze  and  furnished 
inaccurate  data  in  great  number. 

Having  given  (p.  39)  all  the  experimental  data  of  the  five 
combustions  of  Diamond,  by  Dumas,  we  need  here  only 
present  a  summary  of  the  results  of  all  such  combustions 
published  up  to  the  present  date. 

This  reaction  is  atomically  one  of  the  most  sensitive  in 
chemistry,  so  that  four  decimals  here  will  give  a  much  higher 
degree  of  precision  than  five  commonly  used. 

C  O2  :  C  =  44  :  12  =  3.66  667.     Change  2204  low. 
To  4.  decimals  :  3.66  67.       Change  220    low. 

Accordingly,  we  shall  state  all  results  to  four  decimals 
only,  for  carbon.  The  ratio  is  exactly  n  to  3. 

We  shall  also  add  the  total  weight  in  grammes,  of  diamond 
burnt  by  each  analyst. 


102  ABSOLUTE   ATOMIC   WEIGHT. 

Dumas  and  Stas^  1840 : 

5.40  gr.,  5  Det.,  Extr.  95  — 28;  67.     Mean    2  lowc 
.Erdtnann  and  Marchand^  1841 : 

4.83  gr.,  5  Det.,  Extr.  73  —  96;  77.     Mean  30  low. 
Roscoe,  1883: 

6.03  gr..  5  Det.,  Extr.  75  —  49526.     Mean    5  low. 
Friede^  1884: 

1.33  gr.,  2  Det.,  Extr.  40  —  28;  12.     Mean  33  low. 
Mean  of  first  3  sets  of  5  det.  each,  12  low. 

Total  weight  of  diamond  burnt  16.26  grammes  in  these 
15  determinations,  averaging  1.08  grammes  in  each. 

The  four  series  of  determinations  divide  sharply  into 
two  groups,  according  to  the  amount  of  the  analytical 
excesses.  To  obtain  the  corresponding  effect  on  the  atomic 
weight,  we  must  remember  that  a  rise  of  o.i  corresponds  to 
220  low  in  the  fourth  place. 

Hence  Dumas  mean,  2  low,  corresponds  to  12.001 ;  that 
of  Roscoe  to  12.0025. 

The  second  group,  giving  an  analytical  excess  of  about 
"  30  low  "  corresponds  to  about  12.017. 

Since  Dumas  and  Roscoe  used  over  n  grammes  of 
diamond  against  the  others  only  about  half  as  much,  it  is 
evident  that  the  former  had  the  best  chance  of  getting 
accurate  results. 

It  will  be  noted,  that  Friedel  had  only  about  half  a 
gramme  for  each  determination,  while  all  the  others  averaged 
a  gramme  for  each  determination. 

We  must  conclude  that  the  atomic  weight  of  carbon 
(diamond)  is  12  exactly,  within  the  limit  of  the  errors  of 
the  experiment. 

This  limit  is  o.ooi  in  the  case  of  Dumas,  0.002  in  the 
case  of  Roscoe,  and  0.017  in  the  case  of  Erdmann  and 
Marchand,  and  for  Friedel  also. 

This  is  the  simple  record  of  the  facts  ascertained.  It  is 
most  admirable. 

A  False  Correction. 

Recently  A.  Scott  has  called  attention  to  the  effect  of  the 
absorption  of  carbon  dioxide  on  the  volume  of  the  saturated 


CARBON.      DUMAS.  103 


potassium   hydrate.     Journal    Chemical    Society    1897,   pp. 

550-564. 

Taking  all  the  determinations  made  for  "  carbon  "  this 
chemist  now  applies  an  additional  correction,  and  finds  as 
final  umean  value"  C  =  12.0008,  which  even  Ostwald 
concedes  to  bring  the  deviation  from  the  "  round  number" 
12  into  the  region  of  the  errors  of  experiment.  Ztsch.  24, 
P.  3775  1897. 

This  apparent  "  correction  "  has  probably  induced  the 
Three  German  Chemists  (Ostwald,  Landolt  and  Seubert) 
to  put  C  =  12.00  in  the  table  of  the  atomic  weights  adopted 
by  the  German  Chemical  Society  in  1898. 

But  we  most  respectfully  beg  to  object  to  this  correction 
made  en-bloc  for  "  carbon  "  and  for  this  additional  mud- 
dling the  atomic  weight  of  carbon  and  any  such  tt  rounding 
off  "  to  12.00. 

In  thejirst  place,  we  deem  all  such  minute  "  corrections  " 
applied  half  a  century  after  the  publication  of  great  stand- 
ard determinations  of  very  doubtful  propriety.  There  is 
another  gnat  strained  at,  and  another  drove  of  camels  to  be 
swallowed. 

If  an  error  has  been  committed,  let  the  tl  correction  "  be 
made  on  new  work,  but  leave  the  results  of  the  old  masters 
"  uncorrected"  and  undisturbed. 

In  the  second  place  it  is  not  correct  to  apply  any  correc- 
tion to  combinations  of  all  sorts  of  so-called  carbon  for  the 
purpose  of  establishing  the  atomic  weight  of  carbon.  Here 
comes  that  drove  of  camels,  longing  to  be  swallowed. 

Not  even  natural  graphite  can  be  used  for  this  purpose, 
and  the  application  of  artificial  graphite,  is  out  of  the 
question.  Already  Dumas  declared  that  graphite  could  not 
be  weighed  with  absolute  precision.  Compare  p.  48. 

To  include  the  combustions  of  "  sugar  Coal"  and  " paper 
coal"  of  Van  der  Plaats,  1885,  in  the  experimental  data  for 
the  determination  of  the  atomic  weight  of  carbon  is  chem- 
ical folly. 

To  apply  "  corrections  "  to  work  undertaken  with  mate- 
rial which  is  not  fit  to  be  weighed  with  precision,  is  absurd. 


104  ABSOLUTE   ATOMIC   WEIGHT. 

It  is  true  that  Dumas  made  determinations  with  graphite 
as  well  as  with  the  diamond. 

But  the  atomic  weight  which  he  adopts  is  the  one 
determined  by  means  of  the  diamond  only. 

To  prove  this  we  need  only  tabulate  the  determinations 
made  by  Dumas  (and  Stas)  in  1840,  in  our  usual  form  (for 
four  places  only). 

We  shall  add  all  other  combustions  in  the  same  form. 

Combustions  of  Different  Sorts  of  Carbons. 

Dumas  and  Stas  • 

Diamond,               5  Det.,  695  —  628;  67  Mean     2  low. 

Graphite,  Nat'l,   5  Det.,  710  —  670;  40  u  16  high. 

Graphite,  Artif.,  4  Det.,  744  —  654;  90  "  32  high. 
Erdmann  and  MarcJiand : 

Diamond,               5  Det.,  673  —  596;  77  Mean  30  low. 

Graphite,  Nat'l,   3  Det.,  647  —  609;  38  "  29  low. 

Graphite,  Artif.,  i  Det.,  u  39  low. 
Roscoc : 

Diamond,               5  Det.,  675  —  649;  26  Mean     5  low. 

Carbonado             i  Det.,  "  55  low. 
Van  der  Plaats : 

Graphite,                3  Det.,  664  —  663;     i  Mean     3  low. 

Sugar  Coal,           2  Det.,  660  —  655;     5  "  10  low. 

Paper  Coal,           i  Det.,  "  10  low. 

I  deem  it  superfluous  to  add  many  words  to  this  striking 
tabulation  of  the  record. 

The  figures — -giving  a  total  range  of  the  mean,  nearly  one 
hundred — utterly  condemn  any  combination  of  all  these 
determinations  when  the  object  is  the  determination  of  the 
atomic  weight  of  true  carbon. 

For  the  first  condition  in  such  a  problem  is  to  use  the 
purest  material  possible;  that  is  the  diamond,  which  by  its 
very  physical  and  chemical  properties  can  be  handled  and 
cleaned,  as  Dumas  already  accentuated. 

Even  graphite  ii  natural  "  can  not  take  the  place  of  the 
diamond  for  this  purpose — as  also  plainly  implied  in  words 
by  Dumas  half  a  century  ago.  Compare  p.  48,  supra. 


CARBOX.       DUMAS.  IO5 


We  cannot  get  a  general  mean  of  all  determinations 
made  for  carbon,  by  including  any  determinations  of  Van 
der  Plaats,  because  he  made  none  on  purest  carbon,  the 
diamond. 

It  is  perfectly  in  order  to  find  all  determinations  made  on 
any  sort  of  carbon  treated  as  one,  individually  affected  by 
11  probable  errors "  only,  in  the  chemical  olla  fodrida  of 
Clarke,  furnished  by  the  Smithsonian  Institution  of  Wash- 
ington. 

But  it  is  too  bad  for  a  good  English  Chemist  to  apply  a 
minute  correction  to  all  such  determinations  indiscrimi- 
nately and  then  give  us  a  corrected  atomic  weight  of  carbon 
to  the  fourth  decimal  place. 

This  correction,  applied  to  all  sorts  of  carbon,  and  the 
"  corrected  "  result  C  =  12.0008  copied  into  Ostwald's  Zeit- 
schrift  is  really  more  than  even  my  tolerant  nature  could 
stand. 

May  we  not  expect  that  the  chemists  of  to-day  will  use  a 
modicum  of  common  sense  when  handling  the  subject  of 
atomic  weights? 

After  a  patient  and  careful  consideration  of  all  experi- 
mental determinations  made  with  the  purest  material  and 
by  the  most  sensitive  method  of  Dumas,  I  am  convinced  that 
the  atomic  weight  of  true  carbon  does  not  differ  by  as  much 
as  one  thousandth  of  a  unit  from  the  exact  number  12,  the 
atomic  weight  of  oxygen  being  taken  at  16  exactly. 

As  a  most  characteristic  chemical  curiosity  I  translate 
from  page  85  of  Ostwald's  Physik.  Chemie,  Bd.  I,  1891,  the 
following : 

"  There  can  remain  no  doubt  but  the  atomic  weight  of 
tc  carbon  is  to  that  of  oxygen  as  12  to  16,  -within  the  errors  of 
tf  the  experiments,   and   which   may  amount  to   a  few  ten- 
IC  thousandths  of  the  total  value.     We  use  the  value 
"C  =  12.003." 

First  declare  it  is  12  exactly,  within  the  minute  errors  of 
the  experiment;  then  use  a  different  value  throughout  the 
work,  thus  known  to  be  wrong. — uEs  muss  auch  solche 
Kautee  geben." 


K)6  ABSOLUTE   ATOMIC   WEIGHT. 

VIII.     THE  ATOMIC  WEIGHT  OF  CALCIUM. 

The  best  determinations  have  been  obtained  by  using 
purest  calcite,  Iceland  Spar,  as  substance. 

The  first  determinations,  made  by  Dumas,  give  a  mean 
analytical  excess  of  55,  which  would  correspond  to  the 
atomic  weight  C  =  40.055. 

The  determinations  by  Erdmann  and  Marchand  on  spar 
are  very  fine,  giving  a  mean  analytical  excess  of  28,  corres- 
ponding to  Ca  =  40.028.  Their  determinations  on  artificial 
carbonate  bring  the  mean  excess  almost  to  zero,  and  the 
atomic  weight  almost  to  40  exactly. 

On  account  of  the  high  importance  of  these  determina- 
tions we  reprint  the  weighings  from  our  True  Atomic 
Weights,  p.  184,  which  were  copied  from  vol.  8  of  the 
Annales  de  Chimie  et  de  Physique  for  1843. 

In  the  work  of  Clarke,  which  at  least  ought  to  give  the 
data  of  observations  in  full,  these  data  are  horribly  incom- 
plete. Fortunately,  the  volume  of  the  Annales  was  at  the 
Mercantile  Library  of  St.  Louis. 

Ca  O  :  Ca  Oa  C  =  56  :  100  =  0.56  ooo.       Change   100  high. 
Dumas,  1842.     Dissociation  of  Iceland  Spar: 


Weight  in  Grammes. 

Analytical 

No. 

Spar.                Residue. 

Ratio.                  Excess. 

I 

49.916               28.OI6 

0.56  123            93  high. 

2 

50.497               28.305 

053             23  high. 

3 

64.508               36.167 

066            38  high. 

Due  impuritv,  030 

Annales  de  Chimie  et  de  Physique,  III  Series,  T.  S,  p.  202. 
This  excess   would   correspond  to  Ca  40,023  to   40.093; 

mean  40.051. 

Erdmann  and  Marchand,  1842.     Artificial  Carbonate: 


I 

3.2335 

4.6135            0.56  033 

33  I"gh. 

2 

10.8850 

6.0940            0.55  985 

15  low. 

3 

10.1315 

5.6740            0.56  004 

4  high. 

4 

5-53io 

3.0970            0.55  994 

6  low. 

Mean  0.56  004 

4  high. 

Corresponding  atomic  weight  Ca  =  40.004.     Same  volume 
of  Annales,  p.  14. 


CALCIUM.  107 


Erdmann  and  Marchand,  1844.     Iceland  Spar. 

;,*  ,  4.2134  2.3594  0.55  997  3  low. 

2  I5'I385       8.4810       0.56  022       22  high. 

3  23.5503  13.19$$  0-56  031  31  high. 

4  23.6390  13-2456  0-56  <>32  32  high. 

5  42-0295  23.5533  0.56  044  44  high. 

6  49.7007  27.8536  0.56  042  42  high. 

Mean  0,56  028  28  high. 

1850,  i  Det.,  Artif.  Carb.,  0.55  998  2  low. 

This  last  case  made  with  utmost  care.  Combined  with 
the  mean  of  the  four  determinations  on  artificial  carbonate, 
the  general  mean  would  be  i  high,  i  corresponding  to  40.01. 
Ca  O4  S  :  Ca  Os  C  =  136  :  100  =  1.36  ooo.  Change  36  low. 
Erdmann  and  Marchand^  1842.  (Annales  T.  8,  p.  216): 


No. 

Weight  in  Grammes. 
Spar.               Sulphate. 

Analytical 
Ratio.                    Excess. 

I 

2.370 

3-225 

1.36  076 

76  high. 

2 

4.796 

6-5255 

061 

61  high. 

3 

3-065 

4.1690 

020 

20  high. 

4 

5-446 

7.4100 

063 

63  high. 

Mean 

I-36  055 

55  high- 

This  mean  would  correspond  to  39.85. 

For  Ca  =  40,  change  to  S  =  32.1  would  give  ico  high. 

Hence,  55  high  would  correspond  to  S  =  32.055. 

Ca  Ch  :  Ag2  =  in  :  216  =  0.51  389. 
Dumas,  1859.     Volumetric. 

2  — 3  gr.  Det.  5,  Extr.  573  —  394;  179.     Mean  66  high. 

Since  for  40.1  the  ratio  would  be  46  high,  this  mean 
would  correspond  to  Ca  =  4o.i4,  while  the  range  179  corres- 
pond to  a  range  of  0.4  or  one  per  cent  of  the  total  atomic 
weight. 

I  understand  that  T.  W.  Richards  has  also  made  deter- 
minations, probably  on  the  bromide,  as  he  is  wont  to  do; 
compare  his  work  for  Mg,  Sr,  Ba,  Zn.  It  is  all  of  the  same 
general  character. 

The  results  obtained  by  the  dry  and  the  wet  way  differ  in 
accuracy  as  was  stated  in  an  earlier  section,  pp.  46-55. 


IO8  ABSOLUTE   ATOMIC   WEIGHT. 

The  dry  way,  almost  exclusively  used  by  Berzelius,  is  the 
only  way  to  employ  if  the  element  concerned  permits  it. 

The  final  result  is  that  the  atomic  weight,  within  the 
precision  of  the  determinations,  is  40  exactly.  The  experi- 
mental determinations  show  that  the  actual  atomic  weight 
does  not  differ  as  much  as  o.oi  from  the  standard. 

IX.     THE  ATOMIC  WEIGHT  OF  MAGNESIUM.     SCHEERER. 

Marchand  and  Scheerer,  in  1850,  selected  the  purest 
natural  magnesites  for  the  determination  of  the  atomic 
weight  of  magnesium  by  the  direct  dry  way  process,  used  so 
effectively  for  calcium. 

They  selected  three  very  fine  varieties  of  this  mineral. 
A  yellow,  transparent  magnesite  from  Snarum;  a  white, 
opaque  variety  from  the  same  locality  and  a  very  pure,  but 
opaque,  white  variety  from  Frankenstein. 

Chemical  examinations,  made  with  extreme  care,  by 
Scheerer,  revealed  the  presence  of  o.oo  225  of  lime  (Ca  O) 
in  the  Frankenstein  magnesite,  and  o.oo  430  of  lime 
together  with  o.oo  776  of  ferrous  oxide  in  a  unit  of  weight 
of  the  Snarum  magnesite. 

Scheerer  uses  the  results  from  both  localities;  but  we 
deem  such  process  irrational,  because  the  iron  is  likely  to 
change  its  degree  of  oxidation,  and  even  if  it  does  not  under 
the  circumstances,  the  purer  substance  must  always  be 
preferred. 

We,  therefore,  exclude  all  data  obtained  from  the  Snarum 
magnesite,  also  the  first  two  series  of  determinations  made 
with  Frankenstein's  magnesite,  and  use  exclusively  the  third 
series  made  upon  the  purest  material  of  this  fine  variety. 

Now,  the  225  of  Ca  O  found  require  177  CO2  and  con- 
stitute 402  of  Ca  Oa  C  in  the  magnesite  used,  leaving  of 
actual  Mg  Oa  C  only  99  598  —  all  figures  in  fifth  place. 

The  mean  residue  of  the  four  determinations  of  this  third 
series  amounted  to  47  642 ;  since  225  was  Ca  O,  the  true 
Mg  O  amounted  to  47  417  only. 

But  this  in  the  99  598  of  pure  magnesium  carbonate 
amounts  to  0.47  608  per  unit. 


MAGNESIUM.       SCHEERER.  ICM) 

This  value  must  be  considered  as  the  most  reliable 
determination.  The  range  of  the  four  determinations  of 
this  third  series  was  50. 

Now  this  mean  value  of  the  analytical  ratio  is  exactly  n 
low  of  the  atomic  ratio,  which  is 

Mg  O  :  Mg  Oa  C  ==  40  :  84  =  0.47  619.     Change  62  high. 

The  analytical  excess  being  n  low,  corresponds  therefore 
to  the  atomic  weight  0.018  low,  or  say  Mg  =  23.982  or  better 

23-98. 

But  to  state  this  as  the  true  value  would  imply  the  disre- 
gard of  actual  errors  of  the  chemical  work. 

The  range  of  50  represents  an  uncertainty  of  0.08  in  total 
range,  or  perhaps  more  fairly  of  0.04  on  the  mean. 

In  the  summary  of  Clarke  (p.  140)  all  three  series  made 
with  Frankenstein  magnesite  are,  of  course,  combined, 
giving  0.47  628  as  final  mean,  which  is  9  high. 

The  Snarum  magnesite  gives  him  0.47  624,  which  is  5 
high. 

His  final  mean  is  0.47  627,  which  is  8  high. 

Restricting  ourselves,  on  principle,  to  the  purest  material 
used,  makes  our  analytical  ratio  0.47  608,  which  is  n  low. 

The  three  series  made  with  Frankenstein  magnesite 
would  have  given  9  high,  the  Snarum  magnesite  5  high  and 
the  mean  of  all  8  high. 

These  analytical  excesses  correspond  respectively  to  a 
rise  of  0.014,  0.008  and  0.013  on  the  atomic  weight  of  24. 

The  third  series  alone,  made  upon  the  purest  material, 
gave  us  the  analytical  excess  of  n  low,  which  would 
correspond  to  a  lowering  of  the  true  atomic  weight  o.oiS 
below  the  standard  24. 

We  can  therefore  truly  say  that,  taking  the  series  we 
deem  the  most  conclusive,  or  taking  all  or  indeed  any  one, 
the  difference  between  the  true  and  standard  atomic  weight 
cannot  reach  0.02  either  way. 

Accordingly,  the  dry  way  work  on  magnesite,  instituted 
by  Marchand  and  finished  by  Scheerer  fully  half  a  century 
ago,  establishes,  as  a  fact,  by  experimental  work  of  highest 
order,  that  the  true  atomic  weight  of  magnesium  is  not 


iIO  ABSOLUTE   ATOMIC   WEIGHT. 

different  from   the  standard  atomic  weight  24  within  the 
limits  of  precision,  which  may  be  taken  at  0.02. 

Richards'  Determinations. 

Several  other  methods  have  been  tried ;  but  the  alphabet- 
ical record  in  Part  IV,  shows  that  these  methods  were 
defective,  either  in  the  starting  material,  the  final  product 
or  even  in  both,  when  dry  way  processes,  or  they  had  some 
of  these  defects  and  were  made  by  some  much  less  reliable 
wet  way  process. 

It  is  not  necessary  here  to  give  any  of  these  except,  per- 
haps, the  volumetric  process,  rejuvenated  by  Richards,  of 
Harvard. 

Mg  Ch  :  Agz  =95  :  216  =  0.43  982.     Change  46  high. 
Dumas,  1860: 

i  — 4  gr.  Det.  u,  Extr.  380 —  154;  226.     Mean  279  high. 
Richards  and  Parker,  1896: 

Series     II,  Det.  3,  Extr.  152 —  130;  22.     Mean  160  high. 

"        III,  Det.  6,  Extr,  144— 131;   13.         "      156  high. 

"        IV,  Det.  6,  Extr.  138  =  136;     2.        "     155  high. 

Evidently  the  entire  object  of  the  work  of  Richards  is  to 

obtain  concordance  and  with  it  the  praise  of  our  olla  podrida 

maker  in  Washington. 

Richards  Excels  Dumas  4,000  Times. 

This  praise  Professor  Richards  has  received  (p.  144)  in 
the  following  words : 

(<  Here  the  first  two  values  "  (Dumas  and  Series  II  of 
Richards  and  Parker)  "  practically  vanish,  and  the  third  and 
{C  fourth  series  of  Richards  and  Parker  appear  atone." 

The  reason  of  this  high  praise  rests  upon  the  " weight" 
of  the  determinations  always  measured  by  the  inverse  square 
of  the  probable  error  of  the  mean  by  Clarke,  in  his  u  Con- 
stants of  Nature." 

These  probable  errors  are  given  in  units  of  the  fourth 
place  of  the  per  cent,  that  is,  in  units  of  the  sixth  place — the 
millionths  of  the  unit  of  weight — according  to  our  tables. 


MAGNESIUM.       SCHEERER.  Ill 

These  "  probable  errors "  are  given  by  Clarke  on  page 
144  of  the  American  Chemical  Olla  Podrida  as  200,  43,  13, 
3  millionthsper  unit  of  weight  operated  upon. 

The  squares  hereof  are  therefore  400  oo,  1849,  J^9  and  9 
units  in  the  izth  place  or  the  millionth  of  millionths  of  the 
gramme,  per  gramme  operated  upon. 

In  passing,  we  may  state  that  Richards  and  Parker  gen- 
erally used  less  than  two  grammes  of  their  pure  magnesium 
chloride  (they  suppose,  for  it  cannot  be  weighed  accurately) ; 
never  as  much  as  3  grammes. 

Taking  the  relative  values  only,  and  putting  the  skill  and 
perfection  of  the  work  of  Richards  in  his  third  series  at  one 
million,  we  find  according  to  the  process  of  this  same  Olla 
Podrida  Americana,  the  skill  of  the  others  given  as  follows : 
Richards  and  Parker,   IV  Series,  1,000  ooo 
"  "          "         III         "  52  632 

"          II        "  4  878 

Dumas,  1860  only  225 

As  this  table  of  perfection  is  not  quite  readily  grasped, 
we  will  reverse  it. 

We  will  put  the  skill  and  ability  of  the  great  French 
Chemist  Dumas,  as  one  and  calculate  the  skill  of  the 
Harvard  Chemists  in  that  unit. 

In  this  way,  the  above  figures  will  present : 

Skill. 

Chemist  Dumas,  1860,  i 

Harvard  Chemists,      II  Series,        17.5 
"  "  III         "          210 

"  "  IV        «       4,000 

The  chemists  of  Harvard,  "Richards  and  Parker," 
started  out  in  this  atomic  weight  determination  twenty  times 
more  perfect  in  their  work  and  methods,  than  was  Dumas 
almost  at  the  height  of  his  fame. 

Well,  we  may  put  this  twenty  to  the  credit  of  Modern 
Chemistry  and  America;  and  the  modest  young  American 
Chemist  may  not  protest.  The  Present  and  America  is  the 
pedestal  on  which  they  proudly  stand. 

But  just  note  the  wonderful  capacity  for  progress  in  the 
work  of  these  young  chemists  of  Old  Harvard. 


112  ABSOLUTE   ATOMIC   WEIGHT. 

In  their  third  series  the  work  is  200  times  as  excellent 
and  reliable,  according  to  the  Smithsonian  mode  of  calcula- 
tion, than  in  their  second  series. 

In  their  fourth  series  they  have  risen  to  the  exalted  stand- 
ard four  thousand  times  the  capacity  of  Dumas  in  1860,  when 
he  was  considered  the  greatest  chemist  of  the  world. 

And  how  rapidly  our  young  chemists  of  Old  Harvard 
develop,  how  astonishing  the  rate  of  their  progress,  how 
tremendous  the  swiftness  wherewith  they  do  "  evolute!" 

Starting  ({ only  20  times  as  perfect  as  Dumas,"  they  are 
ten  times  surpassing  themselves  in  the  work  of  the  third 
series,  and  two  hundred  times  when  closing  the  fourth  series. 

And  all  this  progress  and  evoluting  done  in  the  space  of 
a  few  months! 

Not  a  word  is  inaccurate  in  the  above,  not  a  figure  or 
proposition  that  is  not  obtained  strictly  according'  to  the 
fundamental  formulae^  pp.  J  and  8  of  the  tl  Constants  of 
Nature,"  produced  by  Frank  Wigglesworth  Clarke,  Chief 
Chemist  of  the  Geological  Survey,  in  the  employ  of  the 
Secretary  of  the  Interior  of  the  United  States  of  America, 
and  published  with  the  endorsement  of  the  Secretary  of  the 
Smithsonian  Institution  at  the  cost  of  the  fund  which  the 
Englishman  Smithson  gave  to  the  United  States  Congress 
for  the  foundation  of  an  it  Institution  for  the  Increase  and 
Diffusion  of  Knowledge  among'  Men  per  orbem» 

Richards  Really  Progressed  0.01  Only. 

The  measure  of  precision  has  been  considered  seriously 
as  it  must  be,  since  we  follow  the  directions  and  formula  of 
a  Government  Publication. 

Now  let  us  see  how  the  final  results  look  when  examined 
as  to  its  absolute  value  according  to  our  standard. 

This,  our  standard,  has  now  been  tested  by  the  atomic 
weights  of  lead,  iron,  mercury,  sulphur,  chlorine,  carbon 
and  calcium,  that  is,  by  the  great  chemical  elements,  great 
in  every  sense  of  the  word. 

These  atomic  weights'  are  based  upon  the  work  done  by 
Berzelius,  Svanberg  (in  the  laboratory  of  Berzelius),  Erd- 


MAGNESIUM.       SCHEERER. 


mann  and  Marchand,  the  best  German  chemical  workers 
in  this  field,  and  Dumas,  the  greatest  French  representative. 

Our  standard  exactly  expresses  the  work  of  these  masters 
under  one  general  formula;  let  us  now  test  the  work  of  the 
young  chemists  of  Harvard,  who  are  by  the  Government 
and  Smithsonian  standard  four  thousand  times  better 
chemists  than  was  Dumas. 

We  see,  by  the  table  of  the  analytical  excess  given  above, 
that  the  analytical  excess  of  Dumas  was  279  high  (in  the  fifth 
place)  ;  that  the  young  chemists  of  Harvard  started  out,  in 
their  second  series  at  about  half  this  excess  (exactly  160)  ; 
that  in  their  third  series  they  brought  this  excess  down  only 
four  additional  units  of  the  fifth  place,  and  in  the  fourth 
series  they  diminished  it  only  by  one  unit  more. 

The  entire  "  Progress  "  they  have  made,  measured 
according  to  our  standard,  is  the  mere  reduction  of  the 
excess  from  160  to  155,  that  is  5  units! 

Now  155  high,  represents  0.34  high  on  the  atomic  weight 
of  magnesium,  putting  it  at  24.34. 

Their  second  series,  160  high,  placed  this  atomic  weight 
at  24.35. 

While  these  young  Harvard  chemists,  according  to  the 
Smithsonian  Institution  and  United  States  Government 
Chief  Chemist,  became  two  hundred  times  more  perfect  in 
precision,  they  only  succeeded  in  paring  off  one  measly 
little  hundredth  from  the  atomic  weight  magnesium,  bring- 
ing it  down  from  24.35  t°  24-34- 

But  these  young  chemists  of  old  Harvard,  and  the  author 
of  the  American  Olla  Podrida  of  Official  Chemistry  in 
Washington  will  say  "  again  "  that  my  standard  is  not  right, 
that  only  Mark  Twain  will  take  it  into  consideration,  and 
what  not  else  of  abuse  and  denunciation  they  may  bring 
forth  when  among  themselves  or  at  the  head  of  some  chem- 
ical fraternity.  See  my  General  Chemistry,  Lect.  99,  Art.  15. 

I  think  we  have  given  enough  of  data  to  show  that  our. 
standard  is  fully  established  by  the  work  of  all  the  great 
masters  in  this  branch  of  chemistry,  even  up  to  this  point. 
We  shall,  in  the  next  few  chapters,  greatly  strengthen  it  by 
the  best  work  done  in  recent  days. 


114  ABSOLUTE   ATOMIC    WEIGHT. 


Scheerer  and  Richards. 

But  entirely  independent  of  all  this,  let  us  for  a  moment 
look  at  the  two  conflicting  results  of  Scheerer  and  Richards. 

Let  us  put  it  in  a  table,  using  the  modern  deadly  parallel 
column  method  which  we  learnt  when  a  boy,  dwelling  with 
Robinson  Crusoe  on  his  lonely  island  in  the  sea. 

Scheerer  Richards. 

Atomic  Weight,  24.00  24-34 

Method,  Dry  Way.  Wet  Way. 

Process,  Ignition.  Titration. 

Substance,  Magnesite.  Chloride. 

Weighable,  Perfectly.  Not  directly. 

Product,  Magnesia.  Silver. 

Weighable,  Perfectly.  Not  directly. 

Difference,  1%  per  cent. 

Finally,  for  this  value  24.34  of  Richards,  the  analytical 
excess  in  the  dry  way  work  of  Scheerer  should  have  been 
211  high;  it  is  preposterous  to  suppose  that  Scheerer  could 
have  been  so  much  in  error  in  dry  way  work. 


Tanagra  Atomic  Weights. 

It  is  not  worth  while  saying  anything  more  about  this 
subject  except  we  might  mention  a  somewhat  parallel  case 
that  has  attracted  the  attention  of  the  public  of  the  United 
States  quite  recently. 

At  Boston,  almost  in  the  shadow  of  noble  old  Harvard, 
they  have  a  Museum  of  Fine  Arts,  which  contained  twentv- 
eight  costly,  rare  and  choice  Antique  Greek  Statuettes, 
known  as  the  Tanagra  Terracottas. 

By  the  news  dispatches  in  the  public  press  of  the  country 
at  the  close  of  November,  1900,  the  people  of  this  land  were 
informed  that  23  of  these  28  Tanagra  Terracottas  had  just 
been  removed  as  forgeries  pure  and  simple. 

According  to  this,  about  5  in  this  quarter  hundred  were 
(at  least  possibly)  genuine,  at  any  rate,  about  twenty  per  cent 
had  not  been  proved  to  be  forgeries. 


PLATINUM.      SEUBERf.  1 15 

It  was  but  natural  for  my  thoughts  to  flit  from  the  Boston 
Museum  of  Fine  Arts  across  the  "  Cam.  Bridge  "  to  the 
Chemical  Laboratory  of  Harvard  University  where  I  visited 
Professor  Cooke  some  thirty-five  years  ago. 

How  happy  the  authorities  of  Old  Harvard  will  have 
reason  to  be  if  twenty  per  cent  of  the  atomic  weights 
recently  manufactured  in  their  Chemical  Laboratory  are  not 
demonstrably  false  and  fraudulent. 

Postscript.  While  reading  the  proof  I  find,  in  Science 
for  July  5,  1901  (p.  36),  the  following  quoted  from  an  article 
written  by  Professor  Richards  for  the  Harvard  Graduate 
Magazine  on  Research  Work  in  Harvard  Chemical  Labora- 
tory. The  italics  are  ours. 

(( In  the  last  ten  years  the  atomic  weights  of  copper, 
"  barium,  strontium,  calcium,  zinc,  magnesium,  cobalt, 
"  nickel,  uranium  and  cesium  have  all  been  studied  with 
"  a  care  which  seems  to  carry  conviction  -with  it.  This  work 
i(  has  all  been  handicapped  by  the  inadequate  quarters  in 
"  which  it  had  to  be  performed,  and  we  now  have  to  face 
"  the  bitter  alternative  of  being  obliged  either  to  turn  atuay 
li graduate  students,  or  else  so  to  crowd  them  together  as 
"to  make  accurate  investigation  almost  impossible." 

It  would  most  assuredly  be  best  for  the  good  repute  of 
Harvard  to  have  this  manufacture  of  Tanagra  Atomic 
Weights  closed. 

Ten  such  Tanagras  in  ten  years  is  too  much.  Our 
Chemical  Rumpelkammer  will  have  to  be  enlarged. 

It  might  be  an  admirable  plan  to  give  Professor  Richards 
a  rest  to  season. 

u  Graduate  Students"  at  Harvard  might  be  "turned 
away  "  into  other  fields  of  chemistry  to  browse,  where  they 
would  do  less  harm  to  themselves  and  be  less  likely  to  dis- 
grace Old  Harvard. 

X.    THE  ATOMIC  WEIGHT  OF  PLATINUM.     SEUBERT. 

The  most  common  and  general  reaction  for  platinum  is 
the  formation  of  the  so-called  double  chloride  with  potas- 
sium or  ammonium  chloride.  This  reaction  is  of  daily  use 


Il6  ABSOLUTE   ATOMIC   WEIGHT. 

in  qualitative  analysis  for  the  detection  of  these  metals  and 
has  been  found  to  extend  to  compound  radicals  and  even 
alkaloids. 

The  most  decisive  and  elegant  method  of  applying  these 
tests  in  microchemistry  is  based  upon  the  wonderful  crys- 
tallizing tendency  of  these  so-called  double  salts. 

The  common  microchemical  test  for  potassium  or  ammo- 
nium by  means  of  the  platinic  chloride  has  all  the  charac- 
ters of  a  first  class  test:  Sensitive,  decisive  and  beautiful. 

The  great  value  of  these  reactions  was  already  recognized 
by  Berzelius  for  atomic  weight  determinations.  In  one 
experiment  he  used  nearly  3  grammes  of  platinum  and 
obtained  an  analytical  ratio  exact  to  the  third  decimal. 

This  reaction  has  been  very  skillfully  used  by  Karl 
Seubert  for  the  determination  of  the  atomic  weight  of 
platinum. 

I  take  great  satisfaction  in  being  able  to  put  the  name 
of  Karl  Seubert  at  the  head  of  this  section,  as  that  of  a 
modern  Chemist  who  has  done  chemical  work  truly  in  the 
spirit  and  according  to  the  methods  of  Berzelius  in  so 
excellent  a  manner  that  I  doubt  not,  his  name  will  remain 
connected  with  the  atomic  weight  of  this  most  remarkable 
modern  metal. 

In  the  future  we  trust  there  will  be  less  determinations 
and  much  better  ones  than  have  been  produced  since  Stas 
demoralized  chemistry  and  Lothar  Meyer  re-calculated 
atomic  weights. 

I  contend  that  the  name  of  the  analyst  at  the  head  of  each 
atomic  weight  will  remain  there,  as  surely  as  that  of  the 
founder  of  a  new  genus  in  botany. 

Seubert  has  produced  the  first  positive  determinations 
permitting  the  establishment  of  the  true  and  absolute  atomic 
weight  of  platinum.  That  fact  cannot  be  changed.  Hence 
that  name  must  stay. 

These  so-called  double  chlorides  are  really  chloro-terna- 
ries;  see  our  general  formulae,  also  in  the  "  Statistik  der 
Krystall — Symmetric  "  presented  by  Haidinger  to  the  Acad- 
emy of  Sciences  of  Vienna,  Sitzungsberichte,  I  Abth.  Bd. 
62,1870 — Typus,  Tetrate ;  IV.  Chloro-salze. 


PLATINUM.       SEUBERT. 


The  proper  names  are  potassium  chloro-platinate, 
ammonium  bromo-platinate,  etc.  We  must  be  permitted  to 
use  these  names  in  this  section. 

The  only  additional  chemical  fact  which  it  is  important 
to  bear  in  mind  is  the  ready  and  complete  decomposition  of 
these  compounds  by  ignition,  leaving  always  the  platinum  in 
the  metallic  state,  the  potassium  as  water-soluble  chloride, 
while  ammonium  and  similar  radicals  are  completely 
volatilized. 

It  is  this  ready  dry  way  decomposition  leaving  the  pro- 
duct in  a  most  admirable  condition  for  exact  weighing, 
ready  production  of  the  substance  in  a  chemically  pure 
crystal  form,  which  first  attracted  the  special  attention  of 
Berzelius  to  the  simpler  members  of  this  group  of  salts  for 
atomic  weight  determinations. 

We  shall  now  give  the  experimental  data  in  our  usual 
form. 

Pt  :  Am2   Cle  Pt  =  195  :  444=10.43  919.     Change  13  high. 

Scubertj  iSSi  : 

Series     I,  Det.  6,  Extr.  963  —  946;  17.  Mean  37  high. 

"        II,  Det.  6,     "      889  —  871518.  "      43  low. 

"      III,  Det.  9,     "      026  —  986;  40.  "      82  high. 

Mean  of  all,                  21  Det.  "       34  high. 

"      "  Series  I,  II,  12  Det.  "        3  low. 

Halberstadt,  1884: 

Reduction,     Det.  10,  Extr.  on  —  880;  131.    Mean  32  high. 

Electrolysis,  Det.    8,    "      979  —  894;    85.       "      15  high. 

Mean  of  all,  18  Det.        "      24  high. 

Pt  :  Ka2  Cl«  Pt=  195  :  486  =  0.40  124.    Change  12  high. 

Seubert,  1881  : 

4  —  7  £*•>  Det-  S,  Extr.  130  —  0705  60.     Mean  17  low. 
Halberstadt,  1884: 

Reduction,     Det.    8,  Extr.  127  —  069;  58. 
Electrolysis,  Det.  u,     u       126  —  0635  63. 

All  19  Det.,  127  —  063;  64.  Mean  26  low. 
Pt  :  Arm  Brc  Pt  =  195  :  711  =0.27  426.    Change  10  high. 


Il8  ABSOLUTE    ATOMIC    WEIGHT, 

Halberstadt,  1884: 

Reduction,     Det.  23,  Extr.  465  —  390;  75. 
Electrolysis,  Del.    9,     «       456  — 386;  70. 

All  Det.  32,     "       465  —  386579.     Mean  3  high. 
Pt  :  Ka2  Bre  Pt  =  195  :  753  =  0.25  896.     Change  10  high. 

Halberstadt,  1884: 

Reduction,     Det.  12,  Extr.  957  —  880;  77. 
Electrolysis,  Det.    6,     "      927  —  877;  50. 

All  Det.  18,     "      957  —  877;  So.    Mean  19  high. 
Pt  :  Pt  Br4  =  195  :  515  =0.37  864.     Change  17  high. 

Halberstadt,  1884: 

Reduction,     Det.    8,  Extr.  873 —  839;  34. 
Electrolysis,  Det.    2,     "      837  —  819;   18. 

All  Det.  10,     "      873  —  819554.     Mean  17  low. 

The  bromo-rlatinates  used  by  Halberstadt  give  a  fine 
confirmation  of  the  work  of  Seubert.  The  Platinic  Bromide 
is  also  valuable. 

In  looking  at  all  these  determinations  we  notice  that 
Series  III  of  Seubert  is  the  only  one  which  conflicts  meas- 
urably with  all  the  others.  As  the  three  series  of  ammonium 
chloro-platinate  differ  in  the  preparation  made  use  of,  we 
are  inclined  to  suspect  that  the  error  was  in  a  lack  of  purity 
of  the  substance  used  for  Series  III.  Its  great  range  also  is 
marked.  At  any  rate,  we  are  fully  authorized  to  throw  it 
out,  as  a  single,  unexplained  conflict  in  over  a  dozen  series. 

The  determinations  of  Halberstadt  for  ammonium 
chloro-platinate  show  a  much  greater  range  than  those  of 
Seubert;  the  analytical  excess  is  also  greater. 

The  most  important  fact  is  that  Seubert  found  the  ana- 
lytical excess  in  the  first  series  high  and  in  the  second  lo-w  to 
about  the  same  extent,  say  about  40,  corresponding  to  0.3  on 
the  atomic  weight  of  platinum  in  either  direction. 

This  is  a  most  important  indication  of  remarkably  close 
work. 

Both  investigators  find  the  analytical  excess  low  for  the 
potassium  chloro-platinate,  to  the  extent  of  from  one  to  two- 
tenths  on  the  atomic  weight  of  platinum. 

As  for  the  ammonium  salt  this  excess  was  generally  low, 


PLATINUM.       SEUBERT.  119 

we  have  here,  in  the  potassium  compounds,  a  distinct  indi- 
cation of  minute  differences  of  deportment  working  in 
opposite  directions. 

The  ammonium  bromo-platinate  comes  out  practically 
exactly  on  the  atomic  ratio,  while  the  potassium  salt  gives 
an  analytical  excess  "  high  *J  or  positive,  corresponding  to 
about  0.2  on  the  atomic  weight  of  platinum. 

It  will  be  noticed  that  the  chloro-salt  of  potassium  was 
"  low  "  to  about  the  same  extent. 

Thus,  combining  such  salts,  differing  only  by  one  ele- 
ment, we  notice  a  compensation  of  the  minute  errors  or 
deviations. 

We  need  not  re-state  that  it  would  be  mathematically 
absurd  to  calculate  the  atomie  weight  from  these  data  taking 
them  to  be  absolutely  exact,  and  then  to  wonder  and  ponder 
how  the  chloro-salt  will  give  a  higher  value  for  the  atomic 
weight  of  platinum,  than  the  bromo-salt,  or  how  the  ammo- 
nium compound  can  give  a  different  atomic  weight  from  the 
potassium  compound. 

The  fact  that  the  sign  or  direction  of  the  analytical  excess 
oscillates  with  the  metal  (Ka,  Am)  or  the  intermediate  (Br, 
Cl),  while  the  numerical  amount  of  this  analytical  excess 
remain  practically  the  same,  shows  that  we  here  simply  are 
at  the  very  limit  of  precision  of  this  kind  of  chemical  work. 

As  now  the  amount  of  this  analytical  excess  corresponds 
to  at  most  two-tenths  on  the  atomic  weight  of  platinum,  it 
is  palpable,  that  the  totality  of  these  experimental  determi- 
nations demonstrate  the  atomic  weight  of  platinum  to  be 
195  exacthr,  which  the  individual  determinations  or  series  of 
determinations  hit  squarely  or  deviate  from  in  either  direc- 
tion to  an  extent  not  exceeding  0.2. 

The  most  excellent  chemical  work  done  by  Seubert  in 
iSSi,  permits  us  to  say  that  the  true  atomic  weight  of  plati- 
num does  not  differ  from  the  standard  value  195  by  any 
fraction  within  the  limits  of  precision  attained,  which  is 
about  0.2. 

All  deviations  from  195  actually  noted,  are  within  this 
limit,  and  about  equally  frequent,  according  to  the  elements, 
positive  and  intermediate,  present  in  the  platinum  salt  used. 


120  ABSOLUTE   ATOMIC   WEIGHT. 

XI.     THE  ATOMIC  WEIGHT  OF  THALLIUM.     CROOKES. 

Praemonitio:  Mr.  William  Crookes,  now  Sir  William 
Crookes,  as  editor  of  the  Chemical  News,  has,  on  two 
occasions,  about  a  quarter  of  a  century  apart,  grossly 
abused  his  position  as  editor  against  me,  and  by  wilfully 
misleading  his  subscribers,  has  defrauded  them. 

About  1868  his  "News"  gave  a  review  of  my  (i Pro- 
gramme der  Atom-Mechanik,"  of  1867,  showing  that  the 
writer  of  that  pretended  review  had  never  read,  probably 
never  seen,  the  book  he  abused. 

After  the  publication  of  my  True  Atomic  Weights  in  1894, 
I  sent  to  Mr.  William  Crookes,  on  September  4,  1895,  a 
complimentary  copy  with  a  letter,  stating  that  the  book  was 
sent  to  him  personally  (not  as  editor,  not  for  revieiv)  and 
referring  to  the  action  above  mentioned,  supposing  that 
some  of  his  writers  had  imposed  upon  him,  it  seeming 
incredible  to  me  that  a  man  in  his  position  could  have 
committed  so  low  an  act. 

That  the  low  act  was  Mr.  William  Crookes'  own,  is  fully 
proved  by  the  ranting  and  denunciatory  review  given  by  this 
same  pettifogging  individual  himself  in  his  Chemical  News, 
vol.  72,  pp.  231-232;  1896.  This  article  had  entirely  escaped 
my  notice,  until  recently,  when  I  looked  up  some  experi- 
mental results  of  Lord  Rayleigh. 

This  shows  that  Mr.  William  Crookes  has  a  very  crooked 
character,  that  can  hardly  be  excused  on  the  ground  of  his 
nauseous  spiritualistic  record. 

After  stealing  the  personal  copy  for  a  u  review "  he 
lacked,  of  course,  the  courtesy  of  sending  me  a  copy  of 
his  manufactured  misrepresentations,  made  deliberately  to 
mislead  his  subscribers.  Such  is  editor  Crookes. 

Is  he  really  too  ignorant  to  comprehend  ? 

It  may,  therefore,  appear  strange  that  I  give  a  position  of 
great  honor  to  this  name  Crookes,  in  line  with  the  greatest 
analytical  chemists,  from  Berzelius  to  Seubert. 

I  hereby  specially  give  notice  that  I  have  exclusively 
reference  to  the  analytical  chemist  Crookes,  and  to  his  own 


THALLIUM.       CROOKES.  121 

laboratory  record  only  after  freeing  the  same  from  the 
blunders,  fraud  and  folly  which  seem  inseparable  from  the 
personality  known  as  William  Crookes. 

The  Atomic  Weight  of  Thallium. 

Ad  rent  :  Under  these  conditions  it  will  be  advisable  to 
determine  the  atomic  weight  of  thallium,  independently  of 
the  earlier  work  of  Crookes. 

There  is  the  electrolysis  of  thallium  sulphate  effected  by 
Lepierre  in  1893.  He  made  3  determinations  on  between 
i  and  3  grammes  of  the  sulphate.  The  extreme  ratios 
run  from  954  to  945,  exhibiting  a  range  of  only  9.  The  mean 
analytical  ratio  is  0.80  953,  which  is  only  i  high,  for  the 
atomic  ratio  is 

Th  :  Th  O4  8  =  408  1504  =  0.80  952. 

The  same  chemist  made  2  determinations  on  between  2 
and  4  grammes  of  thallous  oxide,  which  he  dissolved  and 
submitted  to  electrolysis. 

The  atomic  ratio  for  this  process  is 

Th  :  Th  Oa  =  408  :  456  :  0.89  474, 

while  Lepierre  obtained  in  the  first  determination  13  more, 
and  in  the  second,  i  more ;  his  mean  thus  is  only  7  high. 

Accordingly,  there  can  be  no  doubt  about  the  atomic 
weight  of  thallium.  It  is  204,  exactly. 

We  have  a  number  of  other  determinations,  but  they  are 
mostly  made  according  to  faulty  methods  and  therefore  do 
not  count  here. 

Thus,  the  inferior  silver  chloride  process,  according  to 

Tl  Cl  :  Ag  Cl  =  239.5  :  H3-5  =  i-°6  937, 
gave  Lamy,  1863,  values  differing  in  range  by  938 ;  the  mean 
was  23  low.     Such  determinations  are  worthless,  of  course. 

Hebberling,  in  1865,  obtained  a  mean  472  low,  and  Wells 
and  Penfield,  1894,  obtained  as  mean  405  high.  This  shows 
again  simply  that  the  method  is  bad,  and  that  these  chemists 
did  not  know  it. 

The  reaction 

Tlz  O4  S  :  BaO*  8  =  504  :  233  =  2.16  309, 
has  also  been  used,  but  is  notoriously  far  from  reliable. 


122  ABSOLUTE   ATOMIC   WEIGHT. 

Lamy,  in  1863,  obtained  a  mean  611  high,  in  3  determin- 
ations. 

Hebberling,  in  1865,  also  made  3  determinations;  the 
range  was  nearly  a  thousand  (923). 

All  these  determinations  are  simply  worthless. 

Accordingly,  the  determinations  of  Lepierre  establish 
the  atomic  weight  of  thallium  as  204,  independent  of  any 
work  done  by  Crookes  at  any  time,  before  or  after  the  work 
of  Lepierre. 

We  are  now  able  to  take  up  the  work  of  Crookes  for 
separate  and  independent  consideration. 

Crookes'  Determinations  of  Thallium. 

Ad  hominem:  We  have  no  access  to  the  original  publi- 
cation of  Crookes  in  the  Philosophical  Transactions  for 
1873,  where  it  begins  on  page  277,  according  to  Clarke's 
Constants  (1882,  p.  95,  and  1897,  p.  185),  the  only  record  at 
hand  giving  the  weighings  and  ratios  of  Crookes. 

It  may  be  interesting  to  the  student  to  read  the  general 
statement  of  Clarke  from  this  record.  The  italics  are  ours. 
The  quotation  may  be  read  identically  the  same  in  both 
editions  of  Clarke,  of  1882,  p.  95,  and  of  1897,  p.  185. 

t{  In  1873,  Crookes,  the  discoverer  of  thallium,  published 
"  his  final  determination  of  its  atomic  weight.  His  method 
il  was  to  effect  the  synthesis  of  thallium  nitrate  from  weighed 
"  quantities  of  absolutely  pure  thallium.  No  precaution 
"  necessary  to  ensure  furity  of  materials  was  neglected;  the 
"  balances  were  constructed  especially  for  the  research ;  the 
a  weights  were  accurately  tested  and  their  errors  ascertained; 
"  weighings  were  made  partly  in  air  and  partly  in  vacuo,  but 
u  all  were  reduced  to  absolute  standards;  and  unusually  large 
tf  quantities  of  thallium  were  employed  in  each  experi- 
"ment." 

"  In  short,  no  effort  was  spared  to  attain  as  nearly  as 
a  possible  absolute  precision  of  results.  The  details  of  the 
a  investigation  are  too  voluminous,  however,  to  be  cited  here; 
11  the  reader  who  wishes  to  become  familiar  with  them  must 
"consult  the  original  memoir.  Suffice  it  to  say  that  the 
"  research  is  a  model  ivhich  other  chemists  will  do  vvell  to  coS ' 


THALLIUM.        CROOKES.  123 

So  high  praise  from  that  quarter  we  have  good  reason  to 
deem  a  positive  indication  of  gross  errors  hidden  by  a  pre- 
tentious show  of  extraordinary  precision.  We  shall  find 
these  indications  exact  in  regard  to  the  work  of  Crookes. 
The  chemists  who  have  adopted  this  "  model  "  have  reason 
to  regret  it.  Compare  Ramsay  and  Aston,  under  Boron,  in 
Part  III. 

Every  material  thing,  substances,  balances,  weights,  all 
have  been  most  scrupulously  tested  and  verified,  we  here  are 
informed  through  Clarke. 

But  how  about  the  experimentor  himself,  Mr.  William 
Crookes?  Has  he  been  tested? 

Yes,  the  marvelous  concordance  proves  that  in  the  labora- 
tory he  was  not  "  crooked,"  but  went  the  narrow  path  that 
leadeth  to  the  goal  of  minute  probable  errors.  In  other 
words,  Mr.  William  Crookes  did  agree  very  closely  with  Mr. 
William  Crookes  in  all  laboratory  work  throughout  proba- 
bly many  months. 

But  Chemistry  is  NOT  merely  a  fine  manual  handicraft  of 
the  laboratory  ;  it  is  not  merely  an  Art,  but  is  also  a  Science  ; 
in  my  humble  opinion,  it  is  the  science  of  sciences. 

Have  we  any  assurance  that  Mr.  \Villiam  Crookes,  the 
expert  manipulator  and  chemical  artisan,  was  really  a  chemist 
or  that  Sir  William  Crookes  to-day  has  become  a  real 
chemist,  in  knowledge  and  understanding  as  well  as  in 
weighing,  igniting  and  dissolving? 

I  shall  not  pronounce  judgment  now;  but  examine  his 
work,  which  alone  must  testify  hereto. 

Testing  the  Laboratory  Work  of  Mr.  Crookes. 

The  unit  of  weight  used  by  Mr.  Crookes  is  the  grain. 
The  weighings  are  recorded  to  the  millionth  of  the  grain — 
which  is  almost  down  to  the  hundred  millionth  of  the 
gramme.  There  is  accuracy,  at  least  on  the  face  of  it,  in 
print;  we  shall  come  back  to  this  subject. 

In  this  first  examination  we  next  note  the  amount  of 
metal  used.  It  ranges,  in  the  ten  determinations,  from  12 
to  30  grammes,  being  from  180  to  500  grains  in  the  first 
determination.  Certainly  ample  thallium  was  used,  possi- 
bly too  much,  in  the  first  determination.  We  shall  examine. 


124  ABSOLUTE   ATOMIC   WEIGHT. 

The  ratio  stated  for  100  parts  of  thallium  we  convert,  by 
moving  the  point,  to  our  usual  analytical  ratios ;  here  the 
Amount  of  thallium  nitrate  obtained  from  one  unit  of 
metallic  thallium. 

These  analytical  ratios  are  given  to  6  places.  Droping 
the  last  decimal,  being  visibly  worthless,  and  observing 
common  restrictions,  we  have  our  own  five  place  analytical 
ratios. 

The  mean  of  the  ten  ratios  is  1.30  391 ;  extremes  are  393 
and  388,  giving  a  range  of  only  5  in  the  fifth  place.  That  is 
an  extremely  minute  range.  The  concordance  of  the  deter- 
minations is  truly  remarkable. 

The  chemical  process,  expressed  in  our  Standard  Atomic 
Weights  is 

Tl  Oa  N  :  Tl  1=266  :  204=3  1.30  392.     Chg.  15  low. 

Now  it  is  passing  strange  that  the  analytical  ratio  of  a 
series  of  ten  determinations  made  in  London  in  1873,  should 
within  a  single  unit  in  the  fifth  decimal  agree  with  our 
absolute  atomic  ratio. 

Did  Mr.  William  Crookes  undertake  this  work  to  prove 
that  our  "  theory  "  is  correct?  Hardly,  as  he  but  a  few  years 
previously  had  held  up  to  public  ridicule  our  "  Programme  " 
of  Atom-Mechanics,  while  showing  in  his  abusive  paper 
that  he  certainly  had  not  read  it.  He  simply  tried  to  mis- 
lead his  subscribers  and  thus  to  defraud  them. 

But  really,  the  case  is  still  more  astonishing.  For  upon 
closer  examination  of  the  ratios  we  notice  that  only  the  first 
is  two  below  390;  we  might,  therefore,  exclude  it  as  the  first, 
not  quite  successful  effort  made.  We  want  to  treat  Mr. 
William  Crookes  kindly.  But  at  the  same  time  we  must  say 
that  the  total  weight  of  thallium  used  in  No.  i  is  by  far  the 
highest.  We  shall  have  to  come  back  to  this  point. 

In  ordinary  determinations,  where  even  fine  work  is 
done,  we  would  not  mind  a  variation  of  two  units  in  the  fifth 
decimal.  But  here  we  have  something  extraordinary  indeed 
in  apparent  precision.  Therefore,  let  us  drop  this  deviating 
determination  as  due  to  the  first  trial  of  a  master  workman. 

There  then  remain  9  determinations.  Now  all  9  ana- 
lytical ratios  are  identical  in  the  first  five  digits,  1.3039. 


THALLIUM.        CROOKES.  125 

Thejift/t  decimal  is  twice  3,  thrice  2}  twice  i  and  twice  o. 
The  aggregate  is  14,  mean  of  nine  1.5. 

Hence,  the  mean  analytical  ratio  of  all  10  determinations 
except  the  very  first,  excluded  by  us  for  good  reasons,  is 
1.30  3915,  which  is  only  half  a  unit  in  the  fifth  place  below 
our  atomic  ratio  calculated  from  our  atomic  weights. 

This  mean  analytical  ratio  must  be  considered  absolutely 
identical  tvith  our  atomic  ratio. 

As  the  range  is  also,  for  these  9  determinations,  only  3, 
and  as  these  slight  differences  are  well  distributed,  we  are 
indeed  face  to  face  with  something  remarkably  excellent  in 
apparent  accuracy. 

Since  now  a  rise  of  o.i  in  the  atomic  weight  204  of 
thallium  produces  a  lowering  of  the  analytical  ratio  of  15 
units  in  the  fifth  place,  the  half  a  unit  actually  low  repre- 
sents a  rise  of  only  one  thirtieth  of  such  a  tenth,  that  is  one 
three-hundredth  of  a  unit,  or  only  0.003. 

Taking  the  excess  of  this  analytical  ratio  as  we  find  it, 
the  atomic  weight  of  thallium  corresponding  thereto  would 
be  204.003. 

We  can  therefore  state,  that  the  9  determinations  of  Mr. 
Crookes  of  1873,  demonstrate  the  true  atomic  weight  of 
thallium  to  be  204  exactly,  and  that  the  possible  deviation  is 
not  more  than  three  thousandths  of  a  unit. 

Now  this  is  most  satisfactory  to  me.  Mr.  Crookes  has 
done  a  great  work  for  "my  theory"  which  he  has  abused, 
and  for  our  work  in  general,  which  Sir  William  Crookes  has 
editorially  denounced  like  a  barbarian  and  a  brute. 

Crookes  Annihilates  Sias. 

But  Mr.  Crookes  has  done  much  more  than  this.  He 
has  furnished  us  experimental  determinations  of  the  highest 
order ;  absolutely  and  totally  annihilating  the  entire  System  of 
the  Stasian  Atomic  Weights. 

Now,  Sir  William  Crookes,  in  that  notorious  editorial 
against  me,  declares  himself  once  again  for  this  system  of 
Stas;  coarsely  expresses  his  apparent  hatred  of  me,  because 
I  have  dared  to  show  this  Stasian  System  of  Atomic  Weights 
to  be  wrong,  and  here — he  himself  proves  I  was  right! 


126  ABSOLUTE   ATOMIC   WEIGHT. 

Evidently,  Sir  William  Crookes,  in  1896,  does  not  under- 
stand scientific  chemistry  any  better  than  did  Mr.  William 
Crookes,  in  1873,  when  he  failed  to  understand  the  scientific 
signification  of  his  own  very  good  laboratory  work. 

Just  let  us  see  for  a  moment! 

The  synthesis  of  thallium  nitrate  effected  agrees  to  the 
thousandth  of  a  unit  with  our  standard  atomic  weights. 

In  this  formula  of  the  nitrate  enters  the  standard  atomic 
weight  for  nitrogen  as  only  14  exactly. 

But  Sir  William  Crookes  and  nearly  all  chemists  of  the 
world  adopt  the  Stasian  Value  N  =z  14.04.  They  decide  it 
by  vote.  They  denounce  me  personally  for  showing  Stas  to 
be  in  error.  They  would  burn  me  as  a  chemical  heretic,  if 
they  could. 

Now  a  very  simple  calculation  with  N:rz  14.1,  shows  that 
the  atomic  ratio  will  be  49  high  for  this  change  of  only  o.i 
in  the  atomic  weight  of  nitrogen. 

As  a  matter  of  fact,  the  mean  of  the  9  determinations  of 
Mr.  William  Crookes  is  only  %  a  unit  low  in  the  fifth  place, 
that  is  only  one  hundredth  of  the  tenth  or  one  thousandth, 
making  nitrogen  one  thousandth  low  or  13.999. 

If  Sir  William  will  take  pencil  in  hand  and  read  the 
preceding  paragraph  a  few  times  carefully,  I  hope  he  will 
understand  that  what  we  therein  assert  is  a  very  simple  state- 
ment of  fact,  resting  entirely  upon  the  exquisite  laboratory 
work  of  Mr.  William  Crookes,  and  requiring  only  the 
rudiments  of  mental  arithmetic. 

But  then  the  value  of  Stas  N=  14.04  is  forty  times  as  far 
from  the  truth  as  the  limit  fixed  by  the  laboratory  work  of 
Mr.  William  Crookes,  in  1873. 

And  if  the  value  N  =.  14.04  of  Stas  is  wrong,  the  value 
Ag  zzz  107.92  falls  to  the  ground ;  in  fact,  the  entire  mystic- 
ally— muddy  System  of  Stas*  Atomic  Weights  is  totally 
annihilated  by  Mr.  William  Crookes.  For  all  values  of  Stas 
are  mutually  tied  together;  if  any  one  is  proved  false,  they 
are  all  proved  false. 

This  shows  plainly,  that  Sir  William  Crookes  does  not 
know  'what  he  is  talking-  about  when  he,  in  1896,  comes  to  the 
rescue  of  Stas  and  his  School;  he  forgets  that  a  certain 


THALLIUM.        CROOKES.  127 

plain  Mr.  William  Crookes  published  most  excellent  atomic 
weight  work  in  1873,  of  which,  however,  the  said  Mr. 
William  Crookes  did  not  comprehend  the  meaning,  and  Sir 
William  Crookes  had  not  yet  learned  it  either — in  1896. 

Expurgation  of  Crookes'  Laboratory  Record. 

Before  we  can  make  final  and  safe  use  of  our  above  con- 
clusion, namely  that  the  experimental  laboratory  work  of 
Mr.  William  Crookes  destroys  the  entire  system  of  Stas' 
doctrine  and  all  his  atomic  weights,  we  must  expurgate  the 
record  of  Mr.  Crookes  in  the  Philosophical  Transactions 
from  the  false  and  invented  figures  given  in  Crookes'  last 
three  decimals. 

We  shall  dratv  the  line  at  the  thousandth  of  the  grain. 
That  is  about  half  a  tenth  of  a  milligramme. 

Modern  scientific  writers  delight  in  pointing  out  the 
supposed  depravity  of  priest  and  priesthood  in  early  Christian 
and  in  pagan  times.  They  give  picture  and  word  of  scien- 
tific tricks  played  upon  the  faithful  in  olden  days,  at  Rome, 
at  Athens  and  at  Memphis. 

Will  not  our  modern  exact  scientists,  such  as  for  example 
Sir  William  Crookes,  soon  be  held  guilty  of  more  despica- 
ble depravity  by  this  infinitely  more  criminal  scientific 
trickery  of  their  pretended  exact  determinations  being  even 
less  substantial  than  the  incense  of  the  priests  of  old  ? 

Is  it  not  a  greater  fraud  to  present  to  the  Royal  Society 
a  host  of  numbers,  claiming  to  represent  actual  data  of 
determinations,  made  by  using  our  highest  instrument  of 
precision  in  one  of  its  most  perfect  forms,  when  the 
7iumerals  so  presented  and  thereupon  published  to  the  world 
in  the  big  Transactions  of  that  Royal  Society,  are  palpable 
frauds  and  inventions  to  fully  one  third  of  the  entire  set  of 
numbers  ? 

The  old  priesthood  did  preach  a  mystery,  and  legitimately 
used  many  phenomena,  precisely  as  the  parable  was  used 
about  nineteen  centuries  ago,  and  precisely  as  we  use  certain 
illustrations;  but  modern  science  first  of  all  is  supposed  to 
present  the  facts  of  nature  by  experiment  and  observation, 
and  when  the  pretended  record  of  such  experiment  or  obser- 


I2S  ABSOLUTE    ATOMIC    WEIGHT. 


vation  is  falsified  in  any  way,  a  real  sacrilege  has  been 
committed — as  it  has  been  committed  by  Mr.  William 
Crookes  in  the  glaring  case  under  consideration. 

We  declare  and  shall  prove  all  figures  belotv  the  thousandth 
of  a  grain  to  be  absolute  invention  and  imagination  on  the 
part  of  Mr.  William  Crookes — intention  or  not,  makes  no 
difference  as  to  the  fraud  upon  the  chemical  public  of  the 
world  at  all,  a  fraud  that  has  been  upheld  with  dogged  per- 
sistence for  over  a  quarter  of  a  century,  by  just  such  editors 
of  chemical  journals  as  Mr.  Crookes. 

The  following  table  gives  the  residue  of  fact  as  the  weigh- 
ings, and  also  the  analytical  ratios  as  calculated  by  myself 
from  these  values  exclusively : 

RECORD   OF  WEIGHINGS 
expurgated   by    Gustavus   D.    Hinrichs,    in    1901, 

from  the  record  printed  in  1897, 
by  F.  W.  Clarke,  in  his  "  Constants  of  Nature," 

which  was  declared  to  have  been  copied  from 
TIIK    PHILOSOPHICAL  TRANSACTIONS  FOR    1873  OF  THK 

ROYAL  SOCIETY  OK  LONDON, 
and  which  was  given  as  a  true  copy  of  the 

Record  of  Weighings 

declared  to  have  been  made  by 

Mr.  William    Crookes,  of  London. 


No.  Thallium.  Nitrate.                      Analyt.  Ratio. 

1  497-973  649.295  1.30  388 

3  293- J94  382.304  393 

3  288.563  376-264  393 

4  324-964  423-720  39° 

5  183.790  239.646  391 

6  190-843  248.843  392 

7  *95-544  254.973  392 

8  201.816  263.148  390 

9  295.684  385'544        •  39 1 
10  299.203  390. 1 36  392 

Grains. 


THALLIUM.        CROOKES.  129 


The  only  result  requiring  one  word  of  explanation  is  that 
of  No.  3,  where  my  calculation  gave  2.45  in  the  last  place 
(the  fifth).  I  have  properly  put  this  as  3,  since  the  second 
5  raises  the  first  4  to  5  under  rule.  The  record  of  Crookes, 
as  given  by  Clarke,  gives  2.6,  which  rounds  off  to  3,  exactly 
as  ours. 

Now,  how  do  these,  our  own  calculated  analytical  ratios 
compare  to  those  given  by  Clarke  (and  therefore  by 
Crookes),  pretendedly  based  upon  the  weighing  to  the 
in  in  ion  th  of  the  grain? 

They  are  absolutely  identical  with  the  analytical  ratios 
used  by  us  and  taken  from  Crookes  by  Clarke. 

Hence,  firstly,  all  we  have  said  as  to  the  actual  value  of 
these  ratios  —  and  the  corresponding  true  ivcighings  of  Crookes 
to  the  thousandth  of  a  grain  —  remains. 

The  tme  atomic  weight  of  nitrogen  is  14  and  not  the 
Stasio-Crookes'  value  of  14.04;  all  Stas'  values  are  false, 
according  to  the  expurgated  Crookes. 

They  are  absolutely  identical  —  these  analytical  ratios  of 
ours  with  those  of  Clarke-Crookes; 

Hence,  secondly,  this  constitutes  a  most  absolute  demon- 
stration of  my  declaration,  above  given,  that 

the  three  last  decimals  in  the  weights  given  by  Mr. 
William  Crookes  are  pure  imagination,  absolute 
invention;  that  these  weighings  were  never  made, 
never  had  any  existence  as  experimental  facts,  nor 
ever  were  actually  used  by  Crookes,  for  they  did  not 
enter  his  resulting  analytical  ratios  at  all. 

How  did  Mr.  William  Crookes  get  the  false  weights  he 
submitted  as  experimental  data  to  the  Royal  Society  in 


Of  course,  not  by  the  use  of  actual  weights,  but  by  cal- 
culating the  weight  by  the  oscillation  method. 

Now,  as  we  have  had  to  show  repeatedly,  in  all  such  cases 
of  calculation  it  is  supposed  that  the  calculator  knows  enough 
about  ivhat  he  is  doing  to  stop  when  he  has  reached  the  limit  of 
precision^  and  not  to  go  on  calculating  till  he  gets  tired. 

Mr.  William  Crookes,  in  1873,  was  very  much  younger 
than  now,  and  while  lacking  the  necessary  scientific  know!- 


130  ABSOLUTE   ATOMIC   WEIGHT. 


edge  of  his  actual  degree  of  precision  did  not  easily  get 
tired — but  kept  on  calculating  briskly — till  he  got  three 
places  beyond  the  ken  of  his  balance.  Of  course  he  kept 
eyeing  his  beloved  balance;  he  looked  at  the  fine  machine. 

The  recorded  weighings  contain  9  and  10  digits,  and 
require  ten — place  logarithms  for  calculating  the  analytical 
ratio.  Did  Mr.  Crookes  use  such  tables  ?  Has  he  ever  seen 
such  tables  ? 

If  he  should  claim  that  he  calculated  his  ratios  by  hand 
and  not  by  logarithmic  table,  why  did  he  stop  at  paltry  six 
decimals,  when  10  place  numbers  of  observation  would 
require  10  place  quotients  ? 

In  the  analytical  ratios — the  only  result  of  value  to  us—- 
these three  invented  or  imaginary  decimals  have  entirely 
disappeared  again — without  leaving  the  slightest  trace. 
They  evidently  were  absolutely  spiritualistic  decimals  and 
entirely  imaginary  numerals,  though  they  were  presented  to 
the  oldest  scientific  society  of  the  world  as  data  of  observa- 
tion and  experiment — and  were  so  recorded  and  published — 
and  have  been  so  taken  by  the  Chemical  World,  lo!  these 
thirty  years! 

The  three  last  columns   of  decimals,  presented   by    Mr. 
Crookes,  in  1873,  to  the  Royal  Society  of  London,  as  actu- 
ally observed  weights  of  the  metal  thallium  and  its  nitrate, 
were  absolutely   nothing  but   imagination,  pure  and 
simple,  from  beginning  to  end, 

constituting  an  imposition  on  the   Royal   Society  of 
London,  and 

a  fraud  upon  the  scientific  public  of  the  World. 

Accordingly,  we  find  the  whole  imposition  and  fraud 
very  properly  and  very  naturally  recommended  as  a  model  by 
our  own  scientific  fraud  at  Washington,  in  his  Constants  of 
Nature,  both  editions:  1882,  p.  95,  and  1897,  p.  185. 

And  Sir  William  Crookes,  the  perpetrator  of  this  scan- 
dalous fraud,  rants,  in  1896,  against  me  about  imagination, 
and  what  not;  let  him  first  apologize  to  the  Royal  Society 
for  the  gross  imposition  he  perpetrated  upon  that  august 
body  in  1873. 


THALLIUM.        CROOKES. 


The  Royal  Society  must  Act. 

There  can  not  be  the  slightest  question  about  this  matter; 
the  demonstration  above  given  is  absolutely  complete. 

We  may  add,  that  any  one  having  the  time  to  spare,  for 
a  little  exact-science  amusement  can  take  a  grab-bag,  fill  in 
digits  from  o  to  9  in  about  equal  number,  say  200  of  each, 
and  grab  one  at  a  time,  and  record  it  after  the  digits  given 
in  my  expurgation.  Shake  well  after  each  grab,  and  keep  up 
till  the  three  fraudulent  decimals  expurgated  by  us,  have 
been  replaced  in  number,  all  drawn  from  the  grab-bag. 

These,  u  Crookes'  Decimals  Restored,"  will  be  just  as  val- 
uable and  just  as  worthless,  just  as  crooked  and  just  as  true 
experimental  data,  as  the  original  decimals  foisted  upon  the 
Royal  Society  as  experimental  facts  obtained  by  means  of 
the  fine  balance  of  Mr.  William  Crookes,  "  specially  made 
for  that  research." 

Of  course,  in  grabbing  these  new  crooked  decimals,  there 
will  be  no  objection  to  look  at  that  same  or  any  other  fine 
balance  once  in  a  while  —  it  will  give  a  sort  of  highly  scien- 
tific air  to  this  performance  of  crooked  a  Exact  Science." 

I  hasten  to  disclaim  any  personal  credit  for  this  method 
of  producing  all  the  grandeur  of  ten-place  data  of  observa- 
tion, which  has  filled  our  own  scientific  oracle  Clarke  with 
admiration,  and  made  our  own  Morley  imitate  the  achieve- 
ment in  a  work  published  in  grandest  quarto  style  by  our 
own  Smithsonian  Institution  at  Washington,  in  1895. 

Indeed,  I  believe  the  keen  and  truthful  observer,  Mr. 
Gulliver,  has  reported,  as  an  eye-witness,  something  almost 
as  fine  as  this  grab-bag  exact-science  work  in  his  noted 
travels  abroad.  See  his  Voyage  to  Laputa,  visit  to  first  room 
of  the  Academy,  Division  of  Speculative  Science. 

An  honorable  man  would  hasten  to  apologize  to  me  for 
his  two  editorial  abominations;  a  truly  scientific  man  would 
acknowledge  his  error  and  recall  from  the  Royal  Society 
the  invented  imaginary  data  of  weighings;  but  I  do  not 
think  that  Sir  William  Crookes  is  built  that  way  nor  that  he 
will  act  that  way. 

However,  the  Royal  Society,  having  printed  this  scientific 


ABSOLUTE   ATOMIC    WEIGHT. 


fraud  in  its  Transactions,  will,  I  think,  publish  a  note  of  our 
expurgation  to  set  itself  right  before  the  scientific  public  of 
the  world. 

The  Foundation  of  Modern  Science. 

Modern  Science  rests  on  the  foundation  of  experiment 
and  observation;  it  is  supposed  to  have  superseded  the 
so-called  ancient  use  of  imagination  and  fancy. 

The  record  of  observed  facts  is  therefore  something 
essentially  sacred  to  modern  science;  and  the  Royal  Society 
can  not  evade  its  duty  because  of  the  high  social  standing-  of  the 
culprit,  its  oivn  member,  Sir  William  Crookes. 

If  in  these  modern  days,  the  persons  controlling  scientific 
publications  can  denounce  and  persecute  honest  painstaking 
investigators  who  show  the  error  of  certain  important  data 
used  every  day  in  scientific  work  throughout  the  world, 
while  those  editors  and  other  influential  persons  themselves 
have  published  absolutely  fraudulent  data  of  experiment 
and  observation,  is  not  the  lot  of  the  independent  scientific 
investigator  to-day  worse  than  that  of  the  reformator  of  the 
church  four  centuries  ago? 

The  priesthood  when  forming  a  State  Church  may  have 
abused  its  high  station  of  power  and  responsibility  as  the 
keeper  of  the  Sacred  Truths  of  Religion;  but  neither 
dungeon,  torture,  nor  the  stake  could  prevent  the  final  issue 
so  highly  lauded  by  the  liberal  scientific  public  of  the 
present. 

SCIENCE  is  xo  MORE  SACRED  THAN  RELIGION;  ivhcn 
Official  Science  gets  so  rotten  that  its  record  of  fact  and 
observation  is  rank  fraud,  the  FINAL  ISSUE  is  JOINED. 

Great  ado  has  been  and  continues  to  be  made  about 
impositions  of  relics  of  Saints;  but  how  utterly  innocent 
such  errors  appear  when  contrasted  with  fraudulent  records 
of  observed  facts  of  weighings! 

If  authority  of  official  position  in  State  Science  and  in 
Scientific  Journalism  is  sufficient  to  prevent  just  criticism  of 
data  of  observation  and  experiment,  or  of  conclusion  and 
principle,  the  true  ground  work  of  modern  science  has 
disappeared  from  view,  and  the  errors  and  horrors  of  State 


THALLIUM.        CROOKES.  133 

Science  will  prove  themselves  as  real  and  as  destructive  as 
were  the  errors  and  horrors  of  the  State  Church  in  its  darkest 
days. 

The  Union  of  State  and  Science  (so-called)  of  to-day  is 
rapidly  producing  as  dangerous  consequences  to  the  liberty 
of  conscience  and  the  freedom  of  research,  and  even  to  the 
very  lives  and  reputations  of  modern  investigators,  as  the 
Union  of  State  and  Church  has  been  condemned  for  by  all 
i{  liberal "  writers  since  the  burning  of  Giordano  Bruno  and 
John  Hus. 

The  mental — and  by  necessity  the  moral — depravity 
resultant  can  plainly  be  seen  in  Official  Science  at  Wash- 
ington, by  any  one  who  has  not  closed  his  eyes. 

The  Systematic  Error  of  Crookes. 

We  have  above  excluded  the  first  determination  recorded 
by  Mr.  William  Crookes.  Possibly  Sir  William  may  com- 
plain about  this  rejection  as  a  "  criminal  selection  "  on  our 
part,  and  insist  on  his  record  in  its  entirety.  See  his  fine 
editorial  of  1896,  referred  to  above. 

Being  always  anxious  to  accommodate  my  friends,  I 
cannot  allow  such  a  claim  as  to  discrimination  or  selection 
take  a  shadow  of  footing. 

I  shall,  therefore,  now  take  up  this  No.  i  of  Mr.  William 
Crookes,  and  shall  consider  it  just  as  valuable,  deserving 
just  as  much  confidence,  as  the  other  nine  determinations 
above  specially  considered. 

But  we  have  an  awkward  way  of  looking  at  the  totality  of 
the,  facts  in  every  case  coming  under  our  scientific  consid- 
eration. We  have  shown,  in  our  True  Atomic  Weights, 
that  the  amount  of  matter  used  is  generally  a  very  important 
factor. 

We  shall,  therefore,  now  once  more  consider  all  the  ten 
determinations  published  by  Mr.  William  Crookes  (which 
determinations  we  take  for  granted  comprise  the  total  num- 
ber he  has  made  and  not  a  selection)  and  arrange  them  in 
the  order  of  the  weight  of  the  metal  thallium  used.  We 
need,  for  this  purpose,  only  the  round  number  of  grains. 


134  ABSOLUTE   ATOMIC   WEIGHT. 

The  following  table  gives  the  results: 

Crookes'  Expurgated  Results,  in  the  Order  of  the 
Weight  of  Metal  Used. 

No.  Metal  Used.  Analytical  Ratio. 

5  184  grains.          1.30  391 

6  190   "  392 

7  i95   "  392 

8  201   "  390 

3  289  "  393 
2  293  «  393 

9  296  u  391 
10  299  "  392 

4  325   "  39° 

i  498   "  388 

These  results  show  a  small,  but  very  clearly  marked 
systematic  variation  of  the  analytical  ratio  ^  dependent  upon 
the  amount  of  substance  used. 

Indeed,  Crookes  has  the  same  failing  which  we  showed 
Stas  to  have  been  afflicted  with  in  his  analytical  operations ; 
namely,  his  results  vary  with  the  amount  operated  upon. 
True  Atomic  Weights,  1894,  pp.  80-85. 

We  are,  indeed,  very  sorry  to  detect  the  symptoms  and 
signs  of  this  Morbus  Stasii  in  the  record  of  Mr.  William 
Crookes;  but  the  readers  now  see  it  is  actually  there,  as  a 
fact;  and  I  guess  even  Sir  William  Crookes  will  admit  that 
we  have  diagnosed  this  case  correctly. 

To  allow  for  the  slight  variations  to  which  even  Crookes 
is  entitled,  we  shall  group  these  results  according  to  the 
mean  weight  plainly  marked  in  the  individual  amounts; 
operated  upon.  We  find  the  following  results: 

Nos. 
5^  6,  7,  8 

3;  2 
9,  10 

4 
i 

We  have  added  the  analytical  excess,  in  our  usual  manner 
Here  is  as  plain  and  sharply  marked  a  systematic  varia- 


Mean  Weight. 

Mean  Analyt.  Ratio. 

Excess. 

192  grains. 

1.30  391 

i      low. 

291        " 

393 

I      high. 

298       " 

391-5 

0.5  low. 

325       " 

390 

2        low. 

498       « 

388 

4     low. 

THALLIUM.        CROOKES.  135 

tion  of  the  analytical  ratio,  dependent  upon  the  amount  of 
substance  used,  as  could  well  be  desired. 

How  sad  Sir  William  Crookes  will  be  at  the  sight  of  these 
columns  of  figures,  showing  the  Morbus  Stasii  so  strikingly 
in  the  exquisite  laboratory  work  of  Mr.  William  Crookes 
of  1873. 

The  Morbus  Stasii. 

This  disease  I  have  found  especially  to  affect  analytical 
chemists  who  have  no  broad  knowledge,  but  are  merely  fine 
chemical  operators. 

They  are  artisans,  not  scientists,  in  the  great  domain  of 
Chemistry.  But  they  invariably  believe  they  are  great 
scientists,  and  invariably  denounce  all  who  approach  science 
as  a  sacred  possession  of  the  human  intellect,  on  which  an 
error  of  any  kind  is  a  dark  blot,  and  a  false  statement  of 
fact  an  unpardonable  sin.  For  all  true  science  is  from  God, 
whatever  modern  evolutionists  may  say  to  the  contrary. 

Another  symptom  of  the  Morbus  Stasii  is  the  firm  belief 
of  the  patient  in  his  own  absolute  accuracy.  It  is  true  they 
never  have  themselves  tested  the  accuracy  of  their  work,  for 
the  simple  reason  that  they  do  not  know  how,  being  merely 
routine  men,  common  artisans,  working  in  a  scientific  field, 
in  a  chemical  laboratory. 

The  victims  of  the  Morbus  Stasii  get  raving  mad  when 
any  one  dares  question  their  results,  and  they  abuse  such 
persons  in  the  most  brutal  manner. 

As  the  number  of  artisans  in  the  world,  in  every  line,  is 
much  greater  than  the  number  of  real  artists  and  masters, 
these  victims  of  the  Morbus  Stasii  find  most  sympathetic 
reception  in  the  societies  and  academies;  such  was  the 
experience  of  Stas,  such  is  the  like  experience  of  Crookes. 

Effect  of  Morbus  Stasii  on  Crookes'  Work. 

But  having  pointed  out  the  disease,  let  us  study  its 
gravity  and  its  effects  on  our  conclusions. 

The  column  of  the  analytical  excess  added  in  our  last 
table,  shows  plainly  that  if  Mr.  William  Crookes,  operating 


136  ABSOLUTE    ATOMIC    WEIGHT. 

exactly  as  he  did,  had  used  about  240  grains  of  thallium,  he 
would  have  obtained  our  atomic  ratio  exactly. 

This  would  have  been  the  point  on  the  ascending  curve 
of  his  errors — if  Sir  William  will  for  a  moment  allow  us  the 
use  of  ordinary  scientific  terms. 

On  the  descending  curve  of  errors,  he  would  also  have 
been  able  to  obtain  an  analytical  excess  of  zero,  though  with 
much  greater  difficulty,  as  the  curve  of  errors  (our  trajectory) 
sinks  rather  abruptly.  About  296  grains  would  have  been 
the  most  suitable  weight  to  take  for  repeated  trials,  to  get  a 
mean  excess  of  zero. 

The  trajectory  of  errors  drops  quite  considerably  to  the 
last  point  observed  (500  grains)  ;  but  as  we  have  not  the 
data  of  reduction  to  vacuum,  we  cannot  tell  whether  there 
was  any  deep  pit  or  sudden  very  low  temperature  troubling 
Mr.  Crookes,  at  London,  as  they  have  notoriously  troubled 
his  fellow  sufferer  Stas,  at  Brussels.  Mr.  Crookes  has  not 
taken  us  into  confidence,  so  we  cannot  ascertain  for  ourselves. 

Now,  will  the  effects  of  this  Morbus  Stasii  require  us  to 
modify  our  final  conclusions? 

We  see  the  total  range  is  5  in  the  fifth  place,  and  it  is 
systematic,  continuous,  in  a  definite  curve  or  trajectory. 
(See  True  Atomic  Weights,  1894;  pp.  149-151). 

The  rise  pero.i  on  N  being  equivalent  to  49 — for  which 
we  here  may  take  50 — units  high  in  the  fifth  place,  the  range 
5  corresponds  to  a  tenth  of  o.i,  that  is  to  o.oi  on  Nir:  14. 

The  total  range  or  uncertainty  due  to  the  Morbus  Stasii 
afflicting  Mr.  William  Crookes  in  1873,  amounts  therefore 
to  o.oi  on  the  atomic  weight  of  nitrogen. 

But  this  range  falls  to  both  sides  of  the  truth,  namely, 
from  i  high  to  4  low;  and  this  latter  very  great  depression 
was  due  to  the  patient  having  inadvertently  taken  an 
excessive  dose  of  thallium. 

We  can,  therefore,  assure  Sir  William  that  avoiding 
such  youthful  excesses,  Mr.  William  Crookes  would  have 
committed  no  analytical  excess  greater  than  i  low  in  the 
fifth  place. 

Accordingly,  kindly  excusing  these  thallic  excesses  of  the 
youthful  spiritualist  Crookes,  we  may  say,  that  the  normal 


THALLIUM.        CROOKKS.  137 

excesses  he  committed,  fell  betiveen  one  high  and  one  loiv,  giving 
the  mean  value  the  greatest  possible  force,  and  making  it 
identical  with  our  atomic  ratio. 

This  makes  the  total  range  on  the  atomic  weight  of 
nitrogen  0.002  above  and  below. 

Our  Final  Conclusion. 

Thus,  in  conclusion,  our  diagnosis  of  the  Morbus  Stasii 
of  Mr.  Wm.  Crookes  has  permitted  us  to  add  rather  than  to 
detract  from  the  value  of  his  laboratory  work. 

And  now,  if  Sir  William  Crookes  will  permit  me  to,  I 
will  most  cheerfully  ascribe  all  his  manifestations  of  injustice 
and  brutality  to  the  Morbus  Stasii,  from  which  he  has 
suffered  for  thirty  years. 

If  cured  by  this,  my  somewhat  bitter  medicine,  if  com- 
pletely freed  from  this  really  terrible  disease,  still  affecting 
so  many  official  chemists  in  high  stations,  I  shall  cordially 
congratulate  Sir  William  Crookes  to  the  most  excellent 
analytical  determinations  of  the  nitrate  of  thallium  he  made 
in  1873,  as  plain  William  Crookes,  by  using  reasonable 
amounts  of  the  interesting  and  important  metal  he  had  dis- 
covered. 

And  I  do  hope  that  Sir  William  Crookes,  at  last,  has 
found  out  that  our  science  of  chemistry  is  no  longer 
restricted  to  the  laboratory,  but  reaches  up  into  the  highest 
realms  of  truth  and  wisdom — the  source  of  which  is  God. 

Vain  imaginations  are  not  science,  and  have  no  place  in 
science ;  but  the  ideals  of  truth,  wisdom,  and  of  God,  are  no 
vain  imaginations  and  no  true  science  will  grow  where  these 
ideals  have  been  rooted  out. 

To  present  false  statements  of  facts  is  to  lie  abominably; 
in  the  Science  of  Nature,  to  falsify  in  this  way,  is  to  commit 
a  sin  against  the  Holy  Ghost,  which  is  an  unpardonable  sin. 
It  is  recklessly  committed  to-day,  throughout  the  scientific 
world,  to  the  great  hindrance  of  scientific  progress. 

May  this  chapter  diminish  the  commission  of  this  crime, 
'•  to  the  greater  glory  of  God." 


138  ABSOLUTE   ATOMIC   WEIGHT. 


XII.     THE  BANEFUL  STASIAN  ERRORS. 

I  must  be  allowed  here  to  add  a  few  words  and  to  give  a 
few  figures  which  ought  to  convince  any  chemist  of  the 
utter  rotteness  and  darkness  of  the  muddle  of  Stas. 

Here  we  have — when  stripped  of  the  imaginary  decimals 
— a  great  experimental  work,  giving  most  valuable  results. 

These  results  are  strictly  and  to  the  limit  of  the  high  pre- 
cision of  the  most  excellent  analyst,  Mr.  William  Crookes,  in 
absolute  accordance  'with  our  standard  atomic  "weights* 

The  analytical  ratios  determined  by  Mr.  William  Crookes 
in  1873,  f°r  thallium  to  its  nitrate,  are  worthy  of  a  Berzelius 
endowed  with  the  means  at  the  service  of  Crookes. 

They  leave  no  possibility  of  a  doubt  as  to  the  result;  the 
absolute  atomic  weight  of  thallium  is  204  exactly ;  the  lim- 
iting degree  of  precision  of  actual  determination  is  the 
thousandth  of  a  unit. 

If  standing  alone,  for  this  one  metal  only,  it  would  be 
marvelous.  But  when  we  look  back  and  see  that  the  most 
perfect  chemical  determinations  on  the  purest  materials 
and  by  the  greatest  and  most  conscientious  masters — 
Berzelius,  Svanberg,  Dumas,  Erdmann,  Marchand,  Scheerer, 
Seubert — absolutely  agree  with  this  one  single  set  of 'values , 
our  standard  atomic  weights,  which  here  coincide  also  with 
the  results  of  Crookes  of  1873 — the  evidence  becomes  abso- 
lutely overwhelming. 

The  possibility  that  such  coincidences  could  be  merely  a 
chance,  is  utterly  and  absolutely  zero. 

These  coincidences  are  the  positive  demonstration  of  a 
general  fact,  a  Law  of  Nature,  a  Thought  of  God. 

Our  standard  atomic  weights,  used  as  immutable  stand- 
ards in  all  our  calculations,  so  that  we  stand  on  a  firm 
ground,  on  solid  rock — coincide  throughout  with  the  true 
atomic  weights  determined  by  the  Master  Chemists. 

The  Labyrinth  of  Stas. 

The  atomic  weights  of  Stas — of  his  labvrinthine  group: 
N,  Cl,  Br,  lo,  S,  Pb,  Ag,  Na,  Ka — are  one  and  all  utterly 
false. 


STASIAX    ERRORS.  139 


The  method  of  calculation*  used  by  him  and  by  his 
numerous  Re-Calculators,  makes  it  impossible  that  any  one 
of  these  values  can  possibly  be  true  if  any  other  one  has  been 
proved  to  be  false. 

Surely,  Crookes'  syntheses  of  thallium  nitrate  prove  N  =. 
14.04  to  be  utterly  false. 

Therefore  all  the  values  of  Stas  are  false.  Not  a  single 
one  can  be  true,  if  any  one  single  atomic  weight  of  Stas  has 
been  demonstrated  false. 

Now,  in  this  case  of  thallium,  good,  sufficient  determina- 
tions have  proved  (Lepierre)  Tl  ==  204,  exactly. 

Hence  the  excellent  determinations  by  Crookes  crush- 
ingly  prove  N  =  14.04  utterly  untenable  and  totally  false. 

Thereby  fall  all  the  atomic  weights  of  Stas. 

To  what  extent  chemical  research  and  commercial  analy- 
ses have  been  falsified  will  soon  become  apparent. 

Here  it  may  suffice  to  show  the  error  committed  in  this 
manner  on  the  atomic  weight  of  thallium. 

Crookes  himself  found  the  atomic  weight  so  different 
from  204  or  any  whole  exact  number,  that  he  rested  his  fight 
against  the  so-called  Prout- Hypothesis  on  his  own  excellent 
determinations. 

Mr.  Crookes  did  not  know  that  he  had  falsified  his  splendid 
laboratory  tuork  by  using  the  false  value  of  Stas  for  nitrogen. 

As  practical  chemist,  he  knows  that  if  he  puts  a  one 
thousandth  part  of  strychnine  into  pure  water,  this  water  is 
poisoned. 

He  was  not  sufficiently  versed  in  chemical  science  to 
realize  that  putting  an  error  of  0.04  into  N^  14,  he  falsified 
the  result  of  his  own  labors;  he  poisoned  scientific  truth. 

He  next  poisoned  chemical  literature,  poisoned  his  own 
editorial  spirit,  poisoned  the  very  atmosphere  in  which 
other  chemists  have  to  live,  exposed  to  his  poisonous  pen. 

He  has  held  chemical  science  back  in  the  mud  and  mire 
of  Stas'  labyrinth  by  his  persistent  poisoning  of  all  data  of 
truth  in  his  journal,  and  by  his  constant  attempts  at  the 

*  Compare  that  first  great  humbug-calculation,  by  Strecker,  1846. 
See  Sebelien,  pp.  73-75.  "  The  Method  of  the  Least  Squares." 


140  ABSOLUTE   ATOMIC   WEIGHT. 

scientific  life  and  honor  of  chemists,  like  myself,  who  tried 
to  point  out  that  poison  and  wished  to  remove  the  same. 

Taking    Clarke's    value,    from    the    determinations    of 
Crookes,  exclusively,  (namely  from  ratio  (4)  on  page  187, 
edition  of  1897),  thallium  is  202.595  in  Clarke's   supposed 
Hydrogen  unit;  hence  for  O=  16  exactly: 
Tl  1=204. 139. 

Ostwald  (Physik.  Chemie,  I,  p.  113;   1891)  gives 

11=1204.146 
"  accurate  to  the  second  decimal,"  hence  204.15. 

Both  these  valuations  of  Clarke  and  of  Ostwald,  rest  upon 
the  value  of  N  of  Stas;  each  one  having  " selected"  his 
own  particular  value,  but  it  is  essentially  that  of  Stas,  say 
N  =  14.04. 

The  fraction  0.15  or  0.14  on  T1:=:2O4,  is  taken  to  con- 
demn the  true  values,  that  they  do  not  agree  -with  our 
standard  values. 

Poisoned  water  does  not  agree  with  good  health  or  even 
with  life;  does  that  prove  water  a  poison  ? 

Those  not  hardened  in  the  errors  of  Stas  during  a  life 
time,  and  who  have  not  undermined  their  own  scientific 
standing  with  boisterous  and  continued  declamations  on  the 
excellency,  perfection,  absolute  accuracy,  mathematical 
exactness  of  Stas'  values  and  methods,  will  not  understand 
that  we  do  not  close  our  work  "  right  here."  They  think  we 
have  demonstrated  our  case  completely. 

I  do  not  think  that  my  work  is  done  here.  It  is  true, 
Moses  himself  thought  it  sufficient  to  keep  his  people  forty 
years  in  the  wilderness,  to  get  rid  of  those  unfit  to  live  in  the 
land  of  promise,  and  our  Stasian  Chemists  have  been  in 
such  a  wilderness  for  about  that  length  of  time;  but  by 
means  of  the  crooked  scientific  press,  they  control,  in  these 
press-darkened  times,  it  seems  forty  years  has  not  been 
enough. 

At  any  rate,  tve  shall  not  rest  our  case  at  this  point,  but 
proceed  to  the  consideration  of  the  atomic  weights  of  boron 
and  of  nitrogen,  which  in  a  most  remarkable  manner  con- 
stitute true  and  most  comprehensive  test  cases ,  each  in  its  own 
way,  covering  the  entire  question  in  all  its  essential  rami- 
fications. 


PART  THIRD. 


The  Absolute  Atomic  Weights  of 
Boron  and  Nitrogen. 

A.     EXPERIMENTAL    DETERMINATIONS. 

I.    THE  ATOMIC  WEIGHT  OF  BORON.     RAMSAY. 

The  experimental  work  done  by  Ramsay  and  Aston  is  of 
so  high  an  order  of  excellence  that  we  can,  upon  that  series 
of  determinations  alone,  base  the  absolute  atomic  weight  of 
boron  as  eleven  exactly. 

For  this  reason  the  name  of  Ramsay  is  placed  at  the 
head  of  this  chapter. 

It  would  be  unjust  to  demand  of  a  chemist  more  than 
perfectly  honest  and  reliable  quantitative  determinations, 
which  involve  the  preparation  of  pure  materials  and  the 
management  of  the  actual  operations  with  the  utmost 
attainable  skill. 

The  published  record  of  the  determinations  of  Ramsay 
and  Aston  beai  abundant  testimony  to  the  fact  that  the 
laboratory  work  was  done  in  this  manner.  Journal  Chem- 
ical Society,  v.  63,  pp.  207-217;  1893. 

Ramsay  has  failed  himself  to  obtain  the  true  value  of  his 
determination.  This  is  no  fault  of  his,  but  of  his  school; 
the  individual  cannot  be  blamed  if  he  proceeds  secundum 
artem.  See  pp.  35-36. 

By  our  new  method  we  shall  obtain,  from  these  experi- 
mental determinations  of  Ramsay,  the  true  absolute  atomic 
weight  of  boron  and  even  most  valuable  auxiliary  weights, 


142  ABSOLUTE   ATOMIC   WEIGHT. 

forming  cross-ties,  giving  strength  to  the  entire  system  here 
erected  on  a  field  cleared  of  the  errors  of  Stas. 

The  chemical  process  selected  is  the  warming,  and  sub- 
sequent distillation  of  anhydrous  borax  with  methyl  alcohol 
and  muriatic  acid,  leaving  dry  sodium  chloride  as  residue. 
See  pp.  52-53. 

Both  the  substance  and  the  final  product  are  fixed, 
accurately  weighable  solids. 

The   quantitative  chemical   reaction  is  expressed  in  the 
following  atomic  ratio: 
2  Na  Cl  :  Na2  OT  Bo*  zz:  117  :  202:^:0.57  921.    Chg.  115  low. 

Two  series  of  determinations  were  made.  In  the  first 
series,  flasks  of  not  very  resistant  glass  were  used  and  found 
to  be  attacked  sufficiently  to  vitiate  the  perfect  accuracy  of 
the  results,  giving  as  mean  analytical  ratio  0.57  948  which 
is  27  high. 

This  result  should,  therefore,  not  be  used.  It  has  prop- 
erly been  rejected,  for  cause  stated  as  above,  by  the  experi- 
menters themselves.  Of  course  our  own  Chief  Chemist  put 
this  condemned  morsel  as  a  tit-bit  into  his  fragrant  olla 
podrida. 

For  the  second  series,  flasks  of  very  hard  glass  (combus- 
tion tubing)  were  used  and  the  error,  though  not  absolutely 
avoided,  was  reduced  to  a  very  minute  amount. 

Now  the  sign  of  this  error  is  perfectly  known ;  it  is  an 
increase  of  the  ratio  which,  therefore,  should  come  out 
high,  if  no  other  constant  error  affects  the  process  chosen. 

On  account  of  the  extraordinary  importance  of  this 
second  series  of  determinations,  I  will  transcribe  the  weigh- 
ings from  the  journal  referred  to. 

I  shall,  however,  omit  the  last  two  decimals  of  the 
weights  given  in  the  journal.  These  are  beyond  the  range 
of  positive  determination,  and  therefore  not  experimental 
data.  They  have,  as  a  matter  of  fact,  completely  disappeared 
in  all  reductions  made  by  the  authors  themselves.  I  speci- 
ally call  attention  to  this  fact. 

Probably  it  is  the  recommendation  of  Clarke,  quoted 
under  thallium  that  induced  Ramsay  to  copy  the  model  of 


BORON.       RAMSAY.  143 


Crookes,  abominably  bad  in  this  point.  This  identical 
recommendation  was  made  in  the  first  edition  of  Clarke, 
1887,  P-  95- — We  have  quoted  it,  p.  122,  lowest  line. 

Ramsay  and  Aston's  Weighings,  in  Grammes. 
No.         Na2  O?  Bo4.          Na  Cl.         Analyt.  Ratio.      Excess. 


22 

5-3"  Si 

3.076  12 

0.57  911 

10  low. 

23 

4.780  56 

2.770  05 

943 

22  high 

24 

4.990  74 

2.892  98 

968 

47  high 

25 

4-723  " 

2.736  04 

928 

7  high 

26 

3-3I3  79 

1.918  73 

900 

21  low. 

Extremes  968  —  900;  range  68. 

Mean  0.57  930  9  high. 

It  will  be  observed  that  this  admirable  series  of  analyt- 
ical determinations  deviates  in  the  sense  indicated  (high) ; 
however,  two  of  the  five  determinations  are  low,  showing 
that  the  errors  have  actually  fallen  on  both  sides  of  the 
atomic  ratio! 

It  is  this  last  fact  that  gives  special  value  to  this  series, 
which  also  is  noted  for  the  very  small  constant  error  in  the 
direction  foreseen  by  the  trifling  action  on  the  glass. 

It  will  be  very  interesting  to  obtain  a  more  readily  com- 
prehensive idea  of  the  precision  attained  in  this  work. 

As  stated,  change  of  boron  to  n.i  would  lower  the  ratio 
115.  Accordingly  n.oi  corresponds  to  12  low,  and  11.001 
to  i  low. 

Since  the  individual  determinations  fall  practically  evenly 
on  both  sides  of  our  standard  high  and  low,  bearing  in  mind 
the  minute  constant  error  known  to  make  high,  we  can  say 
that  the  true  atomic  weight  of  boron  is  proved  not  to  deviate 
as  much  as  0.005  from  the  standard  1 1  exactly. 

It  must  therefore  be  recognized  that  the  five  analytical 
ratios  determined  in  the  final  series  of  Ramsay  and  Aston, 
being  determinations  Nos.  22  to  26  inclusive,  authorize  us 
to  declare  that  the  absolute,  true  atomic  weight  of  boron  is 
ii  exactly  (diamond-carbon  being  12  exactly). 


144  ABSOLUTE   ATOMIC   WEIGHT. 

The  Correlation  of  Ratio  and  Atomic  Weights. 

In  the  formula,  above  used,  to  express  the  quantitative 
reaction  employed  by  Ramsay  and  Aston,  we  find,  in. 
addition  to  boron  and  oxygen,  also  the  symbols  of  sodium 
and  of  chlorine. 

We  will  here  re-print  the  reaction  referred  to : 
2  Na  Cl  :  Naz  OT  Bo4  =  117  :  202  =  0.57  921. 

This  relation  is  not  restricted  to  boron,  but  implies  a 
necessary  condition  for  all  the  atomic  weights  represented 
therein. 

We  have  already,  under  the  head  of  thallium,  practiced 
the  work  we  shall  now  explain  a  little  more  fully,  while 
using  it  in  its  broadest  way. 

We  determined  the  exact  atomic  weight  of  nitrogen  by 
the  reaction  devised  for  the  determination  of  the  atomic 
weight  of  thallium.  However,  in  that  case,  we  used 
Lepierre's  determination  for  the  value  of  Tl  and  then  used 
the  syntheses  of  Crookes  for  N. 

But  it  is  evident,  that  we  did  really  not  require  the  work 
of  Lepierre,  and  still  could  have  -verified  both  Tl  and  N  from 
the  determinations  of  Crookes. 

It  is  this  sort  of  work  we  want  to  do  now,  and  for  that 
reason,  we  better  explain  the  mathematical  principle 
employed. 

The  chemical  equation,  re-printed  above,  requires  nr/7the 
chemical  symbols  to  possess  the  values  stated  as  standard 
atomic  weights. 

Hence  the  numerical  values  observed,  namely,  the  ana- 
lytical ratios,  will  form  perfectly  binding  tests  or  conditions 
for  any  one  of  the  true  atomic  weights  of  the  elements  con- 
tained in  that  formula. 

2  Na  Cl  :  Naa  OT  Bo4  =  117.2  :  202.2  =  0.57  962. 

If  we  suppose  Na  to  rise  by  the  usual  one  tenth  of  a 
unit  (o.  i)  "while  all  the  others  remain  constant^  we  shall 
obtain  the  atomic  ratio  0.57  962,  which  is  "41  high,"  as 
compared  to  the  above  given  value  for  Na  =  23. 

2  Na  Cl  :  Naa  O?  Bo4  =  117.2  :  202  =0.58  020. 

In  the  same  way,  for  Cl  =.  35.6,  while  all  the  others  remain 


BORON.       RAMSAY.  145 


constant  and  equal  to  the  standard  values,  we  shall  obtain 
0.58  020,  which  is  "99  high." 

In  fact,  we  might  even  apply  this  same  reaction  as  a  test 
for  the  value  of  oxygen.  Supposing  O  =  16.1  we  shall 

obtain 

2Na  Cl  :  Na2  O  Bo*  =  117  :  202.7  =  0.57  721 
which  value  is  "200  low"  as  compared  to  0.57  921  found  for 
all  standard  values,  including  O  =  16  exactly. 

But  if  a  rise  of  o.i  in  the  atomic  weight  of  oxygen, 
O  =  16,  causes  a  change  of  the  atomic  ratio  of  "  200  low," 
it  is  evident,  that  a  lowering  of  each  single  unit  in  the  fifth 
place  of  the  atomic  ratio  will  correspond  to  a  rise  of  only 
>^oo  of  o.i  in  the  atomic  weight  of  oxygen,  that  is  an 
amount  of  only  0.0005  rising. 

In  general,  it  will  facilitate  the  handling  of  these  minute 
changes,  if  we  will  observe  that  "  change  high  "  corresponds 
to  same  sign,  ' '  change  low  "  to  opposite  signs  of  departure 
and  ratio. 

Accordingly,  the  reaction  practiced  by  Ramsay  and 
Aston  permits  every  one  of  the  four  elements  to  be  tested, 
as  to  the  exact  true  atomic  weight,  provided  we  assume  the 
other  tJiree  constant  or  fixed,  at  their  standard  values  for  the 
time  being. 

The  rates  at  which  these  variations  take  place,  in  the 
fifth  decimal  of  the  ratio  for  an  increase  of  one  tenth  unit 
(o.i)  of  the  atomic  weight  of  the  one  element  specified  is 
given  in  the  following  table,  together  with  its  inverse  calcu- 
lated as  shown  above. 

Change  of  atomic  ratio,  per  o.i  rise  in  atomic  weight;  and 

Change  in  atomic  -weight,  per  rise  of  one  unit  in  fifth 
place  of  atomic  ratio. 

Change  of :  Atomic  Ratio.  Atomic  Weight. 

Boron,  115  low.  o.oo  087  low. 

Sodium,  41  high.  o.oo  244  high. 

Chlorine,  99  high.  o.oo  101  high. 

Oxygen,  200  low.  o.oo  050  low. 

To  readily  follow  the  sign  (high  or  low)  it  suffices  to 
observe,  whether  a  rise  of  o.i  causes  high  or  low,  i.  e.  same 
or  opposite  change. 


146  ABSOLUTE   ATOMIC   WEIGHT. 

Now,  as  a  matter  of  fact,  Ramsay  and  Aston  found  the 
mean  analytical  ratio  0.57  930,  which  we  found  to  be  only 

"9  high/' 

in  the  fifth  place,  notwithstanding  the  fact,  that  the  process 
necessarily  gave  a  trifling  value  high,  due  to  the  action  upon 
even  the  hardest  glass  that  could  be  obtained,  while  the 
actual  individual  values  fell  on  both  sides  of  the  atomic  ratio 
calculated. 

If  we  multiply  the  above  given  values  per  unit  in  the  fifth 
place  by  this  actually  observed  value  "  9  high,"  we  shall 
obtain,  for  each  element  separately,  the  following  possible 
change  in  its  atomic  weight  and  the  corresponding  value  of 

the  latter: 

3  Places.  2  Places. 

Bo  0.0078  low.  10.992  10.99 

Na  0.0220  high.  23.022  23.02 

Cl  0.0091  high.  35-509  35-5 ! 

O  0.0045  low.  15.995  15.995 

In  words,  we  have  thus  established,  that  the  mean  ana- 
lytical ratio  being  "  9  high "  according  to  the  excellent 
analytical  work  of  Ramsay  and  Aston,  proves  that  three  of 
the  four  atomic  •weights  being  exactly  identical  -with  our  stand- 
ard atomic  -weights,  the  fourth  ivill  be, 

if  Boron,       at  most,  o.oi     low; 
if  Sodium,     at  most,  0.02     high; 
if  Chlorine,  at  most,  o.oi     high; 
if  Oxygen,     at  most,  0.005  l°w  5 

This  shows,  for  the  first  time,  the  full  force  of  our  dem- 
onstration, extended  to  all  the  elements  involved  in  any  one 
given  chemical  process  fit  for  atomic  weight  demonstrations. 
I   hope   that  every  chemist  will  readily  understand  this 
method  of  testing,  in  its  broadest  sense. 

The  general  principle  is  easily  stated,  and  I  trust  will 
now  readily  be  understood. 

In  the  chemical  process  here  considered,  we  have  the 
change  of  anhydrous  borax,  Na2  O?  Bo*  =.  202  to  salt,  2  Na 
Cl=  117,  all  atomic  weights  being  taken  as  their  standard 
values,  namely 

Bo  =  n,  Na  =  23,  Cl  35.5,  O  =  16;  exactly. 


SODIUM.       ASTON.  147 


The  standard  atomic  ratio  of  this  process  accordingly  is 
117  :  202=0.57  921. 

Actually  performing  the  operation  five  times  (Nos.  22  to 
to  26),  Ramsay  and  Aston  found  their  mean  analytical  ratio 
"9  high,"  that  is  0.57  930. 

If  this  "  9  high  "  be  ascribed  as  exclusively  due  to 

Bo,  its  atomic  weight  must  be  O.oi    low,    or  10.99; 
Na,    "         "  "  "       "  0.02    high,  or  23.02; 

Cl,     "        "  "  "      "  o.oi    high,  or  35.51; 

O,      "        "  "  "       "  0.005  low>    or  lS-995- 

In  actual  practice,  we  must  arrange  it  so,  that  all  but  one 
atomic  weight  involved  are  determined  beforehand ;  thus  that 
last  one  will  be  determined'by  the  chemical  reaction  used. 

To  the  student  of  higher  mathematics,  we  need  not  say 
that  this  process  is  merely  the  use  of  partial  differentials, 
considering  only  one  of  the  atomic  weights  subject  to  vari- 
ation, at  a  time. 

I  have  also  referred  this  subject  properly  to  the  general 
theory  of  the  variation  of  constants,  so  important  in 
astronomy.  See  True  Atomic  Weights,  1894,  p.  158. 

We  have  purposely  taken  the  entire  amount  of  "  9  high  " 
given  by  Ramsay  and  Aston,  without  change  or  reduction  of 
any  kind. 

But  we  do  know  that  this  value  is  itself  too  high,  as 
indicated  by  the  authors  themselves,  and  as  proved  by  the 
minute  action  on  the  glass. 

Probably  half  this  excess  is  all  that  should  be  taken  into 
account.  Thus  all  departures  would  be  reduced  to  half  the 
values  above  given. 

II.     THE  ATOMIC  WEIGHT  OF  SODIUM.    ASTON. 

We  have  just  seen  that,  if  the  "  high  "  of  the  process  be 
ascribed  to  the  sodium  exclusively,  the  atomic  weight 
thereof  can  only  depart  at  most  0.02  from  the  standard  23 
and  be  "high"  too;  i.  e.  23.02. 

But  we  know,  that  the  action  on  the  glass  accounts  for 
part  of  this  high,  so  that  probably  23.01  would  really  be  the 
limit,  if  the  determination  could  have  been  made  in  abso- 
lutely resistant  glass. 


148  ABSOLUTE   ATOMIC    WEIGHT. 

Thus  we  obtain  a  determination  of  the  atomic  weight  of 
sodium,  which  we  shall  credit  to  Mrs.  Aston,  who  assisted 
Professor  Ramsay  in  that  work. 

Of  course,  this  determination  pre-supposes  that  the 
"  other  three  elements  involved/'  namely,  Bo,  Cl,  O,  be 
known  as  to  their  exact  atomic  weights. 

By  the  general  principle  just  stated,  we  even  need  not 
have  actually  determined  these  values. 

It  is,  I  trust,  fully  understood,  that  the  possible  limit  of 
deviation  is  perfectly  fixed  for  any  and  all  of  the  elements  in 
any  one  reaction. 

But  as  a  matter  of  fact,  we  have  a  good  determination 
for  boron,  independent  of  the  work  of  Ramsay  and  Aston, 
namely,  in  the  boron  carbide  determination  by  H.  Gautier 
in  the  laboratory  of  H.  Moissan,  which  we  shall  refer  to 
presently. 

Consequently,  the  above  determination  for  Naz=r23 
becomes  of  undisputable  force. 

The  Stasian  value,  Na  1^23.05  is  entirely  incompatible 
with  the  "9  high"  of  the  determinations  of  Ramsay  and 
Aston ;  it  would  have  required  a  mean  about  ( i  45  high,"  as 
is  readily  seen. 

Any  such  "high"  is  perfectly  preposterous  in  connec- 
tion with  the  admirable  work  of  Ramsay  and  Aston. 

Since  sodium  has  been  so  completely  kept  inside  the 
Stasian  muddle,  this  determination  here  given  becomes  of 
very  high,  value.  Strange  to  say,  it  is  about  the  only  reliable 
determination  we  can  find. 

Confirmation  of  Cl  =  35.5. 

The  Stasian  value  of  €1—35.45  is  utterly  inconsistent 
with  the  determinations  of  Ramsay  and  Aston. 

Evidently,  the  analytical  excess  should  have  been  "  45 
low"  instead  of  "9  high"  to  warrant  the  Stasian  value. 

Such  an  analytical  excess  is  absolutely  inconsistent  with 
the  work  of  Ramsay  and  Aston. 

Consequently,  this  work  disproves  Stas'  value  for  chlo- 
rine, and  confirms  Turner's  value. 


BORON.      RAMSAY.  149 


The  Silver  Chloride  Process  Tested. 

It  is  a  most  fortunate  circumstance  that  Ramsay  and 
Aston  tried  to  "  check  "  their  analytical  work  by  determining 
the  sodium  chloride  in  their  final  series  (after  weighing) 
also  by  precipitation  with  silver  nitrate,  and  subsequent 
weighing  of  the  silver  chloride  resulting. 

The  atomic  ratio  for  this  additional  determination  is 
Na2  OT  Bo4  :  2  Ag  Cl  1=202  :  287  =  0.70  383. 
Change  to  108.1  gives  ratio  49  low. 

The  weighings  given  (1.  c.  p.  215)  are: 
No.       Na2  OT  Bo4.          Ag  Cl.         Analyt.  ratio.       Excess. 

22  5.311  81  7.525  87         0.70  580  197  high. 

23  4-78o  56  6.779  42  5J7  134  high. 

24  4.990  74  7.080  43  489  106  high. 

25  4.723  12  6.696  02  536  153  high. 

26  3-3J3  79  4-693  J3  6l°  227  high. 

Mean  0.70  546  163  high. 

Accordingly,  the  above  stated  change  foro.i  would  give 
107.67  as  the  atomic  weight  of  silver;  because  163  is  3.3 
times  the  49. 

This  result  conflicts  both  with  the  value  of  Stas  107.93 
and  with  our  standard  108. 

Now,  as  it  fails  to  sustain  the  value  of  Stas,  and  as  it 
greatly  deviates  from  our  atomic  ratios — sustained  through- 
out in  all  the  best  analyses  by  the  best  chemists — it  follows 
that  the  silver  chloride  process  in  the  wet  way,  even  in  the 
hands  of  Ramsay,  gave  unreliable,  false  values,  and  is  unfit 
for  atomic  weight  determinations- 

We  notice  that  Ramsay  (1.  c.  p.  216,  sub.  IV)  tries  to 
connect  this  discordance  with  the  action  on  the  glass;  but 
there  even  then  remained  a  discrepancy  which  to  our  eyes  is 
enormous,  namely: 

Mean  from  sodium  chloride,  10.966 

"         "      silver  chloride,  corrected,         10.997 
Difference,          0.031 
which  amounts  to  one-third  of  one  per  cent. 

The  "  correction  "  applied  by  Ramsay  is  itself  very  ques- 
tionable— the  only  fact  really  demonstrated  is  the  failure  of 
the  silver  chloride  process. 


I5O  ABSOLUTE   ATOMIC   WEIGHT. 

The  discordance  of  these  results  is  even  too  much  for 
Clarke,  who  says  (p.  175),  that  "  the  discordance"  in  the 
ratio  Na  Cl  :  Ag  Cl  ll  -was  noted,  (p.  52)  -which  again  appears 
here"  and  "  entitles  it  to  comparatively  little  credence" 

Now,  a  bad  egg  will  not  hatch,  and  a  bad  analytical  pro- 
cess cannot  give  good  analytical  ratios.  We  should  not  use 
processes  known  to  be  bad  in  determining  atomic  weights 
any  more  than  we  would  set  a  hen  on  eggs  known  to  be  bad. 

Is  it  really  exacting  to  demand  of  a  recalculator  in  the 
government  service  to  use  as  much  intelligence  and  common 
sense  in  the  revision  of  the  atomic  weights,  the  fundamental 
data  of  chemistry,  as  a  farmer  cheerfully  expends  when  set- 
ting a  hen? 

Professor  Clarke  evidently  thinks  such  a  demand  is 
unreasonably  exacting;  for  he  puts  the  five  bad  eggs  of 
Series  I  and  the  five  good  eggs  of  Series  II  under  his  hen — 
and  gets  what  he  always  succeeds  in  getting:  rotten  results 
for  his  fragrant  olla  podrida. 

This  "  discordance"  appears  (on  page  215  in  the  publica- 
tion of  Ramsay  cited)  most  strikingly  under  the  heading  of 

Boron  Atomic  Weight,  Calculated  from: 

No.  Na  Cl. 

22  10.983 

23  -955 

24  .936 

25  .968 

26  .992 
Mean  10.965 

It  is  seen  that  the  two  sets  of  atomic  weights  calculated 
by  the  chemists  themselves  (by  the  use  of  Clarke's  false 
Smithsonian  Atomic  Weights,  see  pp.  33-34,  supra)  are 
irreconciliable;  those  calculated  from  the  silver  chloride 
determinations  being,  on  the  average,  8  hundredths  higher 
than  those  calculated  by  means  of  sodium  chloride. 

Now  "8  hundredths"  is  very  nearly  u one  per  cent"  on 
Bo  =  n. 

A  discordance  of  i  on  100  is  rather  tough  "  Exact 
Science." 


AgCl. 

Differences. 

Hinrichs. 

11.071 

.088 

11.008 

.024 

69 

10.980 

.003 

67 

10.959 

•039 

71 

10.994 

.091 

99 

II.OlS 

11.084 

.079 

I0.992 

BORON.      RAMSAY.  151 


In  the  last  column  I  have  added  my  own  calculation  of 
the  atomic  weight  directly  from  the  analytical  ratio  a  found 
(from  Na  Cl). 

Since,  by  standard  atomic  weights,  the  anhydrous  borax 
is  1584-4  Bo  and  sodium  chloride  is  117,  and  the  analytical 
ratio  is  the  latter  divided  by  the  former,  it  follows  that 
4  Bo  =  q  —  158  where  q  nz  1 17  :  a. 

From  this  expression  our  atomic  weight  given  above  is 
calculated. 

We  notice  that  all  our  values  are  very  near  n  and  oscil- 
late to  both  sides  of  this  number;  the  mean  is  only  8  thou- 
sandths less  than  n. 

The  comparison  of  this  last  column  with  the  first  under 
Na  Cl  shows  strikingly  that  the  constant  error  has  disap- 
peared by  taking  our  standard  values  for  the  auxiliary  atomic 
weights,  namely,  Na  =  23,  and  Cl  =  35.5,  instead  of  the 
Clarke  values  Na  =  23.05  and  Cl  =  35.45,  used  by  Ramsay. 

This  gives  an  additional  demonstration  that  the  com- 
monly used  auxiliary  values  are  false,  and  to  what  an  extent 
their  small  errors  will  affect  the  final  value  of  good  chemical 
determinations.  Compare  page  33. 

It  is,  of  course,  thoroughly  understood  that  we  merely 
wished  to  show  the  effect  of  taking  our  standard  values  also 
in  this  form  of  the  direct  calculation  of  the  atomic  weight. 

We  are,  however,  only  interested  in  the  one  true  absolute 
value  of  the  atomic  weight  of  boron,  which  is  eleven 
exactly,  as  we  have  proved. 

Determinations  by  Henry  Gautier. 

In  the  chemical  laboratory  of  Professor  Moissan,  of  the 
University  of  Paris,  Henry  Gautier  has  recently  made  four 
series  of  determinations  of  the  atomic  weight  of  boron. 

The  results  have  been  presented  by  Moissan  himself  to 
the  Academy  of  Sciences  of  Paris,  and  are  printed  in  the 
Comptes  Rendus,  T.  129,  pp.  595-598  and  678-681  for  1899. 

A  more  complete  record  of  this  work  is  published  on  pp. 
352-382  of  Tome  18,  of  the  Annales  de  Chimie  et  de  Phy- 
sique, Paris,  1899  (direction  includes  Moissan). 

At  the  annual  public  session  of  the  Academy,  on  Decem- 
ber 17,  1900,  the  Vaillant  prize  was  awarded  to  Henry 
Gautier  for  this  investigation  on  the  recommendation  of  the 


152  ABSOLUTE    ATOMIC   WEIGHT. 

entire  section  of  chemistry  (Troost,  A.  Gautier,  Moissan, 
Ditte,  Lemoine),  represented  by  Moissan  as  "  rapporteur." 
See  Comptes  Rendus,  T.  130,  pp.  iiio-ini;  1900. 

It  is  stated  in  this  report  that  the  determinations  of  Ram- 
say, open  to  objections,  made  this  new  research  desirable. 

Thereby  this  section,  in  recommending  the  award,  assert 
that  the  work  of  H.  Gautier  is  superior  to  that  of  Ramsay. 

They  finally  admit  11.01  as  the  value,  and  accentuate  the 
special  discussion  of  the  "  probable  errors  "  by  H.  Gautier. 
See  p.  34,  supra. 

If  this  work  by  H.  Gautier  is  superior  to  that  of  Ramsay, 
we  ought  to  remove  that  name  from  the  head  of  this  chapter 
on  boron.     Let  us  examine  the  work  of  H.  Gautier,  pro- 
duced under  Moissan. 
Henry  Gautier,  1899. 

1.  SULPHIDE:  Change  to  n.i. 
602  Sa  :  Ba  O4  S  =  1 18  :  699  =  o.  16  SSi          20  high. 

Det.  4,  Extr.  897  —  874;  23.  Mean        4  high. 

2.  CARBIDE  : 

Boe  C  :  C  02  — 78  :  44=i-77  273  2360  high. 

Det.  2,  Extr.  293  —  224;  69.  Mean       15  low. 

3.  BROMIDE: 

Bo  Bra  :  3  Ag  Br— 251  :  564  =  0.44  504  10  high. 

I.     Det.  5,  Extr.  516  —505;   n.   Mean  8  high. 

II.     Det.  4,      «       515  —  509;     8.       "  9  high. 

4.  CHLORIDE: 

Bo  Cls  :  3  Ag  Cl  =z  117.5  :  43°-5::=o-27  294    20  high. 

Det.  6,  Extr.  292  —  279;   13.  Mean       10  low. 

Looking  at  the  determinations  as  equivalent  (which  they 
are  not)  we  get,  as  a  first,  general  (though  not  exact)  view, 
the  following  estimate : 

Analytical  Final  Excess.          Atomic  Weight, 

No.          Det.  Excess.  High.  Low.         Mean  Excess. 

144  high  16  0.020  high. 

2  2  15    low  30  0.000   low. 

398  high  72  0.118  high. 

4  6  10  low  60  0.050  low. 

Sums   88  90 

Practically  equal,  high  and  low,  hence  final  excess  zero, 
and  Bo  equal  to  standard  11,  exactly. 


BORON.       RAMSAY.  153 


To  obtain  the  true  excess  on  the  atomic  weight  n,  we 
must  divide  the  excess  of  the  mean,  by  the  change  per  tenth; 
the  quotient  will  be  in  units  of  first  decimal  place. 

The  results  so  obtained  are  stated  in  the  above  table 
under  the  head  of:  atomic  weight,  mean  excess. 

A  mere  glance  at  this  column  shows  that  the  chloride 
and  bromide  give  great  deviations,  that  for  the  sulphide 
being  smaller;  only  the  carbide  gives  less  than  a  hundredth. 

In  this  connection  we  must  bear  in  mind,  that  the  pro- 
cess— the  barium  sulphate  process — used  for  the  sulphide, 
notoriously  is  analytically  very  dull  and  atomically  also; 
2  units  in  the  fifth  place  corresponding  to  o.oi  on  the 
atomic  weight. 

The  chloride  process  is  atomically  as  dull,  and  the  sub- 
stance not  directly  weighable  in  the  sense  of  Berzelius. 

The  bromide  process  is  even  twice  as  dull,  atomically, 
and  the  bromide  equally  unweighable. 

My  Carbide  Process. 

This  leaves  only  the  Carbide  Process  atomically  most 
sensitive  of  all,  and  indeed,  one  of  the  most  sensitive  pro- 
cesses in  chemistry;  but  only  two  determinations  were 
made,  and  these  on  very  small  amounts  of  substance. 

Accordingly  there  is  absolutely  nothing  in  this  research 
of  H.  Gautier  made  under  Moissan,  and  so  highly  honored 
by  the  Academy  of  Sciences  at  the  direct  recommendation 
of  the  same  Moissan,  that  we  must  repell  the  declaration  or 
official  imputation  that  this  research  is  even  comparable  to 
that  of  Ramsay. 

Tested  by  our  methods,  which  were  publicly  taught  in 
the  halls  of  the  University  of  Paris  by  Schutzenberger  under 
the  presidency  of  Friedel  as  far  back  as  1896.  (Actualites 
Chimiques,  pp.  4-17;  1896,  also  his  standard  work:  Chimie 
Generale,  Paris,  1898,  pp.  143-152),  and  repeatedly  repre- 
sented in  the  Comptes  Rendus  and  in  my  work  "The  True 
Atomic  Weights,  1894,"  so  well  known  at  Paris,  we  find 
nothing  (with  one  exception)  in  either  the  method  of  work 


154  ABSOLUTE   ATOMIC   WEIGHT. 

or  in  the  results  obtained  by  H.  Gautier  comparable  in  value 
to  the  work  of  Ramsay  which  this  is  intended  to  supplant  or 
to  support. 

The  one  exception  referred  to  is  the  carbide  process, 
which  was  borrowed  from  pp.  175-176  of  my  True  Atomic 
Weights,  1894,  in  the  hands  of  Moissan,  and  favorably 
known  throughout  the  scientific  circles  at  Paris,  as  I  could 
readily  prove  by  fac-simile  letters  of  prominent  members  of 
several  sections  of  the  Academy  of  Sciences  of  Paris. 

Even  if  Moissan  had  overlooked  this  most  important  part 
of  my  book,  he  and  his  section  of  chemistry  must  have  been 
reminded  of  it  by  the  very  pointed  second  paragraph  of  my 
paper  in  the  Comptes  Rendus  T.  131,  pp.  1712-1714;  1900, 
published  six  months  before  the  section  reported  to  the 
academy  in  December,  1900. 

This  entire  communication  of  mine  "  On  the  True 
Atomic  Weight  of  Boron"  is  printed  at  the  close  of  this 
chapter,  in  literal  translation  from  my  French  original, 
printed  June,  1900,  in  the  Comptes  Rendus. 

In  thus  ignoring  my  work,  while  making  use  of  my 
method,  the  section  has  not  treated  me  as  dishonorably,  as 
it  has  two  of  its  own  leading  members  whom  three  of  said 
members  have  followed  to  the  grave  barely  a  couple  of 
years  ago. 

La  Pleiade  de  Chimistes  d'Alsace. 

These  two  great  chemists,  Schiitzenberger  and  Friedel, 
together  with  Wiirtz  and  the  officially  so  much  persecuted 
*  Gerhardt,  constitute  that  famous  "  Pleiade  of  chemists  of 
Alsace"  (and,  therefore,  German  in  real  origin  as  well  as  in 
name)  so  generally  counted  in  as  French  chemists,  for 
example,  by  Lemoine  in  his  admirable  eloge  of  Friedel, 
spoken  on  July  23,  1900,  before  the  academy. 

Why  should  the  public  teachings  of  these  great  men  be 
treated  with  contempt  by  Moissan  and  his  present  associates? 

And  if  my  work  were  unworthy,  if  these  last  chemists 
of  the  "  Pleiade  of  chemists  of  Alsace  "  had  been  mistaken 
in  their  public  teaching  at  the  University  of  Paris,  and  in 

*  See  his  biography,  by  his  son  and  Grimaux,  published  in  1900. 


BOROX.       RAMSAY.  155 


the  endorsement  of  my  principles,  why  should  Moissan  use 
my  method,  the  carbide  method,  the  only  one  which  is  good 
in  the  four  employed  by  his  student,  and  say  nothing 
about  it? 

Does  Monsieur  Moissan  believe  that  he  can  commit  such  an 
act  without  the  chemical  world  taking  notice  thereof? 

Monsieur  Henri  Moissan. 

This  carbide  method  is  fully  set  forth  in  my  book  of 
1894,  the  page  cited  in  the  Comptes  Rendus  for  June  18, 
1900;  the  method  is  direct,  connecting  atomic  weights  to 
my  standard  of  matter,  the  diamond,  by  oxygen  as  the  only 
link,  common  to  all. 

To  make  matters  worse,  Moissan  let  the  very  excellent 
young  chemist,  Henry  Gautier  waste  his  time  and  skill  on 
the  crude  and  dull  methods  of  his  own  (see  p.  47,  last  3 
paragraphs,  supra) ,  while  he  had  him  use  my  method,  exact 
and  sharp,  only  on  two  determinations  and  upon  very  small 
amounts  of  the  carbide. 

The  precise  chemical  method  of  reaching  the  combus- 
tion, removing  by  liquid  chlorine  the  boron,  is  worthy  of 
Moissan,  and  cheerfully  recognized  by  me ;  but  the  method 
of  atomic  weight  determination  used,  he  has  taken  from  my 
publication,  without  giving  due  credit  therefore. 

Finally,  Moissan  has  caused  his  special  laboratory  student, 
Henry  Gautier,  to  falsify  his  most  excellent  laboratory  "work 
by  reducing  the  same  by  means  of  the  false  German  atomic 
weights.  See  p.  34,  supra. 

I  have,  in  my  paper  of  June  18,  1900,  which  now  follows, 
and  which  I  supposed  sufficiently  clear  and  comprehensible 
to  any  chemist,  and  especially  in  the  next  paper,  shown  up 
this  falsification  and  therefore  spoliation  of  excellent  French 
laboratory  work  by  false  German  standards,  selected  by 
Moissan. 

If  the  "  new  era"  of  French  chemistry  under  Monsieur 
Henri  Moissan  shall  continue  in  that  way,  French  chemists 
will  suffer  much  more  than  I  by  the  dishonorable  and  over- 
bearing manner  in  which  Monsieur  Moissan  has  acted  and 
forced  his  colleagues  to  cover  his  action  with  their  name. 


156  ABSOLUTE   ATOMIC   WEIGHT. 

His  dishonorable  treatment  of  his  dead  colleagues,  the 
last  of  the  Pleiade  of  Chemists  of  Alsace,  I  leave  to  his  living 
confreres  to  deal  with. 

How  utterly  ignorant  of  all  chemistry,  not  merely  manual 
in  character,  Moissan  must  be,  is  palpably  evident  in  the 
prominence  given  in  his  Rapport,  accentuating  the  "  prob- 
able errors"  having  been  determined  and  ll  discussed,'"1 
when  as  a  matter  of  fact  he  thei^eby  shows  that  he  does  not 
even  know  how  that  useless  humbug  (see  pp.  n-iS)  is  cal- 
culated; see  p.  363  of  the  "  Annales  "  above  cited,  where 
the  essential  coefficient  (nearly  %)  is  omitted,  so  that  all 
the  " probable  errors"  calculated  and  discussed  are  50  per 
cent,  too  high! 

I  hasten  to  conclude  "  cette  affaire"  by  stating  in  as  plain 
words  as  I  can  command,  that: 

I.  The  analytical  work   of  Ramsay  for  the  determina- 
tion of  the  atomic  weight  of  boron  is  conceived  in  the  spirit 
of  Berzelius  and  was  carried  out  in  a  manner  equally  high, 
and  that  as  a  matter  of  fact,  it  permits  us  to  establish  the 
atomic  weight  of  boron,  as  we  have  shown. 

II.  The  three  methods  proposed  by  Moissan  are  either 
notoriously   dull  analytically  (sulphide)  or  are  contrary  to 
the  Berzelian  spirit  (substance  not  weighable,  use  of  silver 
process,  etc.)  and  give  enormous  departures  of  from  5  to  12 
hundredths  on  the  atomic  weight  of  only  n; 

III.  My  carbide  method  is  good,  gives  excellent  results, 
but  has    been    neglected    in    favor  of    his   own   miserable 
methods;   and  Moissan  has  insulted  the  memory  of  his  late 
colleagues  as  well  as  myself  by  taking  my  method  without 
giving  due  credit  therefor. 

Friedel  and  Schutzenberger. 

That  I  have  a  perfect  right  to  connect  these  honored 
names  of  the  "Last  of  the  Pleiade  of  Alsace"  with  my 
own,  will  require  no  word  of  proof  in  the  circles  of  la  Haute 
Academie  des  Sciences,  which  I  honor  and  respect  most  highly, 
and  from  many  leading  members  of  which  I  hold  tokens  of 
regard  and  encouragement;  but  for  the  benefit  of  the  general 


BORON.       RAMSAY.  157 


scientific  public  and  especially  for  the  younger  chemists,  I 
will  add  the  following  few  special  facts,  which  to  state  the 
circumstances  fully  entitle  me : 

Friedel,  for  several  years,  habitually  addressed  me  as  his 
friend  (ami)  and  treated  me  as  such;  I  knew  him  personally 
since  1873. 

In  1896  he  accepted,  with  cordial  thanks,  the  dedication 
of  my  General  Chemistry,  published  early  in  1897;  see  pp. 
5-9  of  that  work.  And 

Schutzenberper,  in  his  published  lectures  and  in  his  great 
work  on  General  Chemistry,  as  above  specified,  has  pro- 
nounced himself. 

Indeed,  one  of  the  professors  of  the  University  of  Paris, 
recently  wrote  me:  "  Schiitzenberger  avait  une  admiration 
veritable  pour  vos  ide"es." 

Of  Friedel,  the  honorable  successor  to  his  "  fauteuil " 
in  the  academy,  declared,  when  taking  that  chair,  (July  23, 
1900): 

"//  avait  la  foi:  foi  dans  ses  opinions  chimiques; 
"  foi  aussi  dans  ses  opinions  philosophiques  et  dans 
"  les  devoirs  pratiques  qu  'elles  imposent."* 

This  man  of  faith,  as  well  as  of  science,  was  greatly 
depressed  after  November  15,  1897,  and  died  a  little  over  a 

year  after  that  date.  Those  who  can  read may  find 

the  reasons  in  the  Comptes  Rendus  of  that  date. 

His  whole  scientific  and  personal  character  was  rudely 
shaken  by  an  assault  on  the  atomic  theory  on  the  part  of  a 
noted  chemist  who  himself  has  ornamented  the  pages  of 
the  Comptes  Rendus  with  numerous  of  the  imaginary  dia- 
grams of  Emil  Fischer  of  Berlin.  This  assault  was  seconded 
by  another  leading  chemist. 

It  is  scarcely  thirty  years  since  Dumas  acted  that  way; 
"c'est  toujours  la  m6me  chose"  —  only  the  names  have 
changed.  O  temporal  O  mores! 

*  He  was  a  man  of  firm  convictions,  of  faith;  conviction  in  his 
chemical  opinions;  conviction  also  in  his  philosophical  opinions  and  in 
the  practical  duties  which  they  impose. 


158  ABSOLUTE   ATOMIC   WEIGHT. 


On  the  True  Atomic  Weight  of  Boron.* 

"  The  substance  which  must  be  taken  as  standard  of  matter 
for  the  fundamental  data  of  Chemistry,  the  Atomic  Weights, 
is  the  Diamond ;  C  =  12,  exactly.  See  :  Apergu  du  Syste"me 
des  Poids  Atomiques  de  precision,  fonde*  sur  le  diamant 
comme  matiere  e*talon  (Comptes  Rendus,  T.  117,  pp.  1074- 
1078;  1893.) 

"The  crystallized  carbides  produced  by  Mr.  Moissan 
have  suggested  to  me  an  entire  series  of  direct  determina- 
tions of  precision.  See :  True  Atomic  Weights,  pp.  175-176, 
Saint  Louis;  1894. 

u  Mr.  Henry  Gautier  has  recently  made  the  first  two  deter- 
minations of  this  kind,  in  the  Laboratory  of  Mr.  Moissan. 
Comptes  Rendus,  T.  129,  pp.  595-598;  1899. 

"  In  the  first  determination,  268.6  milligrammes  of  boron 
"carbide  gave  him  151.5  mgr.  of  carbon  dioxide;  in  the 
"  second  determination,  326.8  mgr.  of  carbide  gave  him 
«'  184.4  dioxide." 

"  In  order  to  avoid  the  introduction  of  errors  in  the 
"  calculation  or  by  the  use  of  auxiliary  data  which  might  be 
"  inexact,  it  is  best  to  proceed  according  to  my  General 
{i  Method  for  the  Calculation  of  Atomic  Weights,  published 
"  in  the  Comptes  Rendus,  T.  116,  pp.  695-698;  1893." 

"The  common  atomic  weight  of  boron  being  n,  the 
unit  of  weight  of  the  carbide  (Boe  C  =  78)  must  give  0.56  410 
of  the  dioxide  (COa  =44). 

"According  to  the  first  determination,  the  268.6  of 
carbide  ought  to  have  given  151.52  mgrs.  of  dioxide,  which 
is  0.02  mgrs.  more  than  the  value  obtained  by  Mr.  Gautier. 

"  In  the  second  determination,  the  268.6  mgrs.  of  carbide 
ought  to  have  given  184.34  mgrs.  of  dioxide,  or  0.06  mgrs. 
less  than  the  amount  found  by  Mr.  Gautier. 

"  Since  these  minute  deviations  are  entirely  below  the 
limit  of  the  weighings,  it  follows  from  the  determinations 
of  Mr.  Henry  Gautier  that  the  common  atomic  weight  of 

*This  is  a  correct  and  complete  translation  of  my  paper  published  in 
the  Comptes  Rendus,  T.  131,  pp.  1712-1714;  1900. 


NITROGEN'.       LORD    RAYLEIGH. 


boron  is  also  its  true  atomic  weight.  See  Comptes  Rendus, 
T.  116,  p.  695;  1893. 

<f  The  application  of  my  general  method  of  calculation 
gives  us  a  true  appreciation  of  the  excellency  of  the  labora- 
tory work  made  by  Mr.  Henry  Gautier;  besides,  we  were 
right  in  our  confidence  in  the  great  value  of  the  crystallized 
carbides  of  Mr.  Moissan  for  the  direct  determination  of 
atomic  weight  by  means  of  carbon. 

"  Mr.  Gautier  has  also  made  several  determinations  on  the 
sulphide,  chloride  and  bromide  of  boron.  By  the  method 
of  the  means  and  the  use  of  German  values  of  the  auxiliary 
elements,  he  obtains  as  many  values  for  the  atomic  weight 
of  boron,  and  finally  adopts  the  number  11.016  (1.  c.  p.  681). 

"By  applying  our  general  method  to  the  experimental 
data  of  Mr.  Gautier,  we  find  the  mean  11.004,  which 
indicates  that  the  true  value  must  be  1 1  exactly. 

lt  In  addition,  the  laboratory  work  of  Mr.  Gautier,  in  this 
our  direct  reduction  and  without  any  hypothesis,  demon- 
strates that  the  German  data  used  in  the  calculations  of 
Mr.  Gautier  present  several  errors.  We  shall  return  to  this 
subject." 

This  is  my  full  communication  as  printed  in  the  Comptes 
Rendus,  of  the  meeting  of  the  Academy,  held  on  June  18, 
1900. 

The  report  of  the  Section  of  Chemistry  often  referred 
to,  was  made  at  the  meeting  of  December  27,  1900,  fully 
half  a  year  later. 

This  gives  the  essential  data  under  consideration  as  they 
are  on  record  in  this  official  organ  of  the  Academy  of 
Sciences,  of  Paris,  the  Comptes  Rendus. 


III.    THE   ATOMIC   WEIGHT  OF   NITROGEN.     LORD    RAYLEIGH. 

The  name  at  the  head  of  this  chapter  is  not  that  of  a 
chemist,  in  the  common  acceptance  of  that  term.  The  Right 
Honorable  Lord  Rayleigh  is  Professor  of  Natural  Philoso- 
phy of  the  Royal  Institution  of  Great  Britain ,  London. 

But  Lord  Rayleigh  has  produced  the  experimental  deter- 
minations which  enable  us  to  establish  the  true  value  of  the 


l6o  ABSOLUTE   ATOMIC   WEIGHT. 

atomic  weight  of  nitrogen,  and  to  demonstrate  beyond  the 
shadow  of  a  doubt  that  the  value  of  Stas,  N=  14.04,  is 
absolutely  false. 

We  may  say,  the  error  of  Stas  and  his  school  led  to  the 
discovery  of  argon,  which  discovery  in  turn  proved  the 
absolute  fallacy  of  the  results  proclaimed  by  Stas  and  so 
viciously  maintained  by  his  school. 

Density  Determinations  and  Atomic  Weights. 

The  density  of  true  gases  is  proportional  to  their  molecu- 
lar weight;  and  hence,  for  gases  of  like  molecular  constitu- 
tion, this  density  is  directly  proportional  to  their  atomic 
weight. 

From  the  earliest  times,  density  determinations  have, 
therefore,  justly  been  considered  most  valued  auxiliaries  in 
atomic  weight  determinations. 

The  density  determinations  of  nitrogen  were  used  as 
most  valued  confirmation  of  the  Stas'  atomic  weight 
N  ==  14.05. 

In  the  first  edition  of  the  u  Constants  of  Nature,"  1882, 
p.  50,  we  find  the  following  table  of  results  for  O  zz:  15.96  to 
which  we  add  the  values  corresponding  to  the  common 
standard  O  r=  16.  We  also  arrange  the  results  in  the  order 
of  their  magnitude. 

Atomic  Weight  of  Nitrogen.     (Clarke,  1882). 

No.                                      For  Oxygen.  15.96  16.00 

5  Ka  Nitrate,  13.97  74  14.012 
4  Ag      "  13-98  40  14-019 

6  Na      te  13.99  °6  14.026 

1  Density,  14.02  44  H-°59 
3            Am  Glide  to  Ag  Nate,              14.03  30  14.068 

2  Am  Glide,  14.03  36  14.069 

General  Mean,  14.02  91  14.064 

Range,  actual,  0.05  62 

u        per  unit,  o.oo  40 

We  see  here  really  three  distinct  values  of  the  atomic 
weight  of  nitrogen ;  we  fail  to  see  how  Clarke  can  notice 


NITROGEN.       LORD    RAYLEIGH.  l6l 

any  "  remarkably  close  agreement M  or  really  any  agreement 
for  a  fundamental  atomic  weight  which  is  pretended  to  have 
been  established  with  marvelous  accuracy. 

We  see,  as  a  matter  of  fact,  a  loiv  value  from  the  nitrate, 
about  14.02 ;  a  high  value  from  the  chlorides,  about  14.07 ; 
and  a  medium  value  from  the  density,  14.06. 

The  latest  most  accurate  density  determination  before 
the  discovery  of  argon  was  published  by  Lord  Rayleigh 
(Journal  Chemical  Society,  vol.  64,  pp.  514-515;  1893).  We 
give  the  actual  weights  in  grammes  per  liter  and  divide  by 
the  standard  atomic  weights  16,  14  and  i  to  get  the  value  for 
the  standard  ONE  : 

Grammes  per  Liter.  Per  Unit  Atomic  Weight. 
Oxygen,                             1.42  961  0.08  935 

Nitrogen  (atmosph.),    1.25  749  0.08  982 

Hydrogen,  0.08  991  0.08  991 

We  notice  that  the  atomic  weight  appears  not  strictly 
proportional  with  the  density,  for  the  weight  per  unit  of 
atomic  weight  is  least  for  oxygen  and  greatest  for  hydrogen. 
This  will  be  found  to  be  a  sign  of  chemical  impurity, 
according  to  late  researches. 

If  we  calculate  the  atomic  weight  of  nitrogen  from  the 
observed  densities  here  given  (Lord  Rayleigh's,  of  1893),  we 
obtain : 

Oxygen,  taken  at  16  exactly. 

Nitrogen,  I4-°7  34 

Hydrogen,  i.oo  62 

Lord  Rayleigh's  Discovery. 

But  Lord  Rayleigh  discovered  that  nitrogen  obtained  by 
strictly  chemical  means  from  ordinary  chemical  compounds, 
which  gas  he  termed  chemical  nitrogen^  invariably  gave  a 
decidedly  lower  density  than  when  he  operated  upon  atmos- 
pheric nitrogen,  that  is,  nitrogen  from  the  air — all  operations 
understood  to  be  conducted  so  as  to  obtain  pure  products, 
secundum  artem. 

This  permitted  only  one  conclusion,  namely,  that  one  or 


l62  ABSOLUTE   ATOMIC   WEIGHT. 

both  of  these  forms  oipure  nitrogen  secundum  artem  contain 
some  material  not  jet  known  (impurity)  in  the  then  state  of 
the  chemical  art. 

Investigation,  carried  on  by  this  master,  assisted  by  the 
chemist  Ramsay,  led  to  the  separation  of  argon  from  the 
air.  Argon  is  much  heavier  than  nitrogen,  but  not  removed 
from  it  by  the  purifying  absorbents  in  use  prior  to  1894  in 
chemical  art. 

The  density  determinations  of  Lord  Rayleigh,  published 
in  1897  (Chemical  News,  v.  76,  315),  for  atmospheric  air  as 
unit,  are  copied  in  the  next  table,  to  which  I  have  added  a 
column  of  atomic  weights  for  O  =  16  exactly.  Of  course, 
for  air  and  atmospheric  nitrogen  this  number  must  only  be 
taken  as  a  density  referred  to  O  r=  16. 

Density.  Atomic  Weight. 

Air,  free  from  H2  O  and  C  O2,        i.oo  ooo  H-47  51 

Oxygen,  O2,  i.io  535  16.00  oo 

Nitrogen  (atm.)  with  Argon,  0.97  209  14-07  n 

<;         (chem.)  no  Argon,  0.96  737  14.00  27 

Hydrogen,  0.06  960  i.oo  28 

Argon,  1.37  752  19.91  97 

Jahrbuch  d.  Chemie,  1898,  p.  4,  quotes  from  Proceedings 
Royal  Society,  v.  62,  pp.  204-209,  the  following  molecular 
weights,  for  O2  —  32  : 

Nitrogen,  N2  28.060 

Carbon  Oxide,  C  O,  27-999 

Carbon  Dioxide,  C  O2,  44.268 

From  these  data  we  learn,  that  pure  nitrogen,  free  from 
argon,  has  an  atomic  weight  of  14.003  only,  according  to 
Lord  Rayleigh's  density  determination. 

Incidentally  we  notice  that  hydrogen  is  1.003  onty>  als° 
that  by  subtracting  the  one  oxygen  from  the  carbon  oxide, 
we  obtain  as  atomic  weight  of  carbon  11.999. 

Now,  since  this  last  value  is  true  (within  the  limit  of 
precision),  namely,  conform  to  the  results  obtained  by 
Dumas  and  his  followers  by  the  combustion  of  the  diamond, 
the  true  atomic  weight  of  nitrogen  can,  according  to  Lord 
Rayleigh's  determinations,  not  deviate  more  than  0.003 
our  standard  value  of  14  exactly. 


NITROGEN.       LORD    RAYLBIGH.  163 

Also,  hydrogen  only  0.003  from  the  standard  of  I 
exactly. 

But  the  values  of  14.04  (Stas)  or  the  mean  of  1882  in 
Clarke,  namely,  14.06  deviate  respectively  40  and  60  thou- 
sandths, instead  of  only  3  thousandths. 

Hence  the  value  of  Stas,  namely,  N=  14.04,  is  irrecon- 
ciliable  with  the  most  accurate  weighings  of  pure  oxygen 
and  pure  nitrogen  made  up  to  1897,  by  Lord  Rayleigh. 

Accordingly,  we  maintain  that  these  experimental  deter- 
minations of  the  density  of  nitrogen,  made  by  Lord  Rayleigh 
in  1897,  demonstrate  the  falsity  of  Stas*  value  of  14.04.. 

Density  Recognized  for  Atomic  Weight  Determination. 

In  the  edition  of  the  Smithsonian  Atomic  Weights  of 
1882,  the  density  value  falls  between  the  values  deduced 
mainly  from  Stas'  determinations  by  chemical  means — and 
Clarke  uses  the  density  determinations  ex  asquo  with  the 
chemical  determinations  in  his  mean  for  nitrogen,  as 
quoted  above,  p.  160. 

Since  the  density  determinations  were  much  more  con- 
cordant than  the  vaunted  exquisitely  and  marvelous  chemical 
determinations  of  Stas,  the  "probable  error  "  of  the  density 
determinations  was  the  smallest  of  all,  only  0.004,  while  the 
probable  errors  of  the  means  of  the  chemical  determinations 
ran  from  15  to  22,  or  were  from  4  to  5  times  as  large. 

Accordingly,  the  chemical  determinations,  namely  by 
Stas,  were  from  16  to  25  times  (the  squares  of  4  and  5)  less 
reliable,  than  those  obtained  from  density  determinations, 
according  to  the  valuation  of  Clarke. 

Therefore  the  weight  of  the  density  determinations  being 
about  twenty  times  as  great  as  the  weight  of  the  chemical 
determinations  in  the  Clarkian  sense  (we  might  properly 
say,  in  a  truly  Pickwickian  sense),  the  general  mean  adopted 
by  Clarke  is  nearest  the  density  value,  and  Stas1  -work  is 
really  excluded  by  Clarke  ! 

On  page  47  of  the  edition  of  1897,  we  read  concerning 
determinations  made  by  the  most  admirable  Marignac  and 


164  ABSOLUTE   ATOMIC   WEIGHT. 

by  our  own  Huntington  and  by  the  famed  manufacturer  of 
Tanagra  Atomic  Weights  at  Harvard  University,  as  con- 
trasted with  those  of  Stas  on  bromine : 

"  In  this  case  again,  as  in  so  many  others,  Stas'  work 
(e  alone  appears  at  the  end,  the  remaining  data  having 
•'  only  corroborative  value." 

The  exclusion  of  the  above  chemists  in  favor  of  Stas,  is 
simply  due  to  the  fact  that  Stas  kept  his  u  probable  error  " 
down  to  6  in  the  fourth  place  of  Clarke,  while  the  other 
chemists  above  named  had  allowed  their  "•  probable  errors" 
to  run  up  from  30  to  70. 

But  since  these  lf  probable  errors  "  are  from  5  to  12  times 
as  large  as  those  of  Stas,  the  weight  or  the  reliability  of  the 
results  of  Stas,  will  be  from  5  X  5  =  25  to  12  X  I2  =  *44 
times  as  high  as  that  of  the  other  chemists  in  the  Pickwick- 
ian Sense  of  Clarke. 

But  for  these  other  chemists  to  count  for  anything  in 
competition  with  Stas,  they  would  have  had  to  produce  from 
25  to  150  times  as  many  determinations  as  were  furnished 
by  Stas. 

Since  they  did  not,  they  were  cooly  a  dropped  "  out  ll  at 
the  end." 

Now,  why  did  not  Clarke  in  the  case  of  the  atomic 
weight  of  Nitrogen  above  quoted  (p.  160)  "  drop  out  Stas 
at  that  end?" 

Why  did  not  Clarke  Drop  Stas  at  the  End? 

And  why  insist  on  the  excellence  of  Stas,  when  de  facto 
the  atomic  weight  of  nitrogen  proclaimed  in  the  Smithsonian 
Pickwick  of  1882,  was  not  based  upon  Stas — being  excluded 
on  account  of  the  four  times  greater  probable  error — but 
upon  the  density  determination  of  what  then  was  supposed 
to  have  been  pure  nitrogen? 

And  as  the  density  determination  was  the  most  reliable, 
giving  the  smallest  probable  error,  why  was  it  discarded 
when  found  to  be  vitiated  by  a  big-  constant  error,  which 
affected  it  notwithstanding  its  deliciously  minute  probable 
error  ? 


NITROGEN.       LORD    RAYLEIGH.  165 

Simply  because  the  Smithsonian  Publications  in  question 
are  not  presenting  true  science  resting  on  observed  facts, 
but  the  Pickwickian  form  so  much  more  palatable  to  the 
capacity  of  Official  Scientists  at  Washington. 

Now,  in  the  second  edition  of  the  Smithsonian  Atomic 
Weights,  the  density  values  of  1882,  having  proved  to  be 
greatly  in  error,  and  the  new  and  correct  density  determina- 
tions by  Lord  Rayleigh  being  absolutely  irreconciliable  with 
the  chemical  determination  of  Stas,  does  Clarke  recognize 
the  experimental  fact  and  discard  the  experimentally  dis- 
proved and  condemned  atomic  weights  of  nitrogen,  resulting 
from  the  chemical  determinations  made  by  Stas? 

Nothing  of  the  sort;  he  simply  absolutely  disregards  the 
experimental  work  of  Lord  Rayleigh,  because  he  has  long 
ago  become  a  blind  believer  in  the  extreme  accuracy  and 
perfection  of  the  chemical  determinations  of  Stas,  to  such 
an  extent,  that  he  does  evidently  not  even  know  that  the 
determinations  of  Stas  are  themselves  mutually  irreconcili- 
able! Only  under  boron  (p.  175)  he  gives  a  slight  indication 
of  discomfort  about  certain  "  discordances."  See  p.  150, 
supra. 

He  merely  says,  that  on  account  of  the  presence  of 
argon,  the  former  determinations  of  the  density  (and  hence 
the  atomic  weight)  of  nitrogen,  were  "all  too  high,  and 
"  unavailable  for  any  discussion  of  atomic  weights,"  see 
1.  c.,  p.  60. 

This  sentence  is  rather  mixed  up,  and  has  only  a  Pick- 
wickian sense  as  it  stands  in  the  book.  It  really,  de  facto, 
implies  that  the  work  of  Lord  Rayleigh  is  "  unavailable." 

Clarke  adds  a  few  lines  further  on : 

"  Perhaps j  at  some  future  time,  when  the  density  of  argon 
"  is  accurately  known  and  its  amount  in  the  atmosphere  has 
u  been  precisely  determined,  these  figures  may  be  so  corrected 
"  as  to  be  useful  for  atomic  weight  calculations." 

"  These  figures  "  are  the  older  ones,  including  those  of 
Lord  Rayleigh  of  1893.  But  the  conflict  established,  the 
error  should  have  been  conceded.  Lord  Rayleigh  has 
corrected  the  older  values,  as  shown,  by  removing  the  argon. 

Having  in  my  True  Atomic  Weights  of  1894,  with  great 


l66  ABSOLUTE   ATOMIC   WEIGHT. 

care  and  at  very  considerable  length,  shown  that  the  deter- 
minations of  Stas  are  conflicting  and  false  in  themselves, 
not  even  complying  with  the/>.s/  and  fundamental  condition 
of  all  analytical  work,  to  give  ratios  (or  percentages)  inde- 
pendent of  the  amount  of  matter  operated  upon,  I  shall  not 
devote  any  great  space  in  this  volume  to  the  fossil  chemical 
errors  of  Stas. 

We  shall  rather  show  the  utter  falsity  of  the  pretended 
high  concordance  of  the  determinations  of  Stas  in  one  of 
the  subsequent  chapters,  after  having  shown  once  again, 
that  they  really  do  not  even  approach  to  a  constant  value, 
but  vary  greatly  with  the  amount  of  substance  operated  upon. 


Density  Determinations  by  Leduc. 

Apparently  very  accurate  density  determinations  have 
been  made  by  Leduc  of  Paris,  both  for  nitrogen  and  for 
oxygen,  which  fully  corroborate  the  results  obtained  earlier 
by  Lord  Rayleigh. 

But  this  apparently  excellent  laboratory  work  by  Leduc 
is  mixed  up  with  such  absurdities  and  such  a  lack  of  knowl- 
edge of  the  simplest  general  principles  of  chemical  science, 
that  I  confess  to  a  doubt  about  the  value  even  of  the  experi- 
mental work. 

The  Comptes  Rendus  (Tome  123,  p.  807;  1896),  give  as 
the  results  of  the  actual  weighings  of  Leduc  the  following  in 
grammes  per  liter.  We  add  the  quotient  obtained  by  our- 
selves per  unit  of  standard  atomic  weighty  in  dividing  the 
oxygen  value  by  16,  the  nitrogen  value  by  14. 

Per  Standard 
Grammes  per  Liter.  Unit  of  At.  Weight. 

Oxygen,  1.42  93  0.08  933  i 

Nitrogen,  1.25  07  0.08  933  5 

To  the  fifth  place,  these  quotients  are  identical. 

This  proves  that  the  densities — and  hence  also  the  atomic 
weights — of  nitrogen  and  oxygen  are  exactly  commensura- 
ble, being  in  the  exact  proportion  of  the  numbers  14  to  16, 
within  the  errors  of  determination  (to  five  places  full). 


NITROGEN.       LORD    RAYLEIGH.  167 

Taking  the  density  of  oxygen  at  exactly  16,  these  weights 
give  the  density  of  nitrogen  14.0007. 

Hence  for  O  =  16  exactly,  these  weighings  give 
N  =  14.0007. 

The  possible  departure  of  the  atomic  weight  of  nitrogen 
is  accordingly  less  than  o.ooi  from  our  standard  value  of 
14  exactly. 

We  have  used  these  determinations  of  Leduc  in  our  Gen- 
eral Chemistry,  1897,  p.  378. 

So  much  for  the  experimental  work  of  Leduc. 

Now  let  us  look  at  the  other  side,  to  ascertain  whether 
Leduc  is  scientifically  reliable. 

Leduc's  Atomic  Weights. 

This  is  the  richest  thing  in  atomic  weights  which  I  have 
found  yet;  it  was  presented  to  the  Academy  of  Sciences  of 
Paris  by  Professor  Lippmann,  on  August  2,  1897.  See 
Comptes  Rendus,  T.  123,  pp.  299-301 ;  1897. 

The  beginning  and  closing  of  this  communication  are 
too  characteristic  of  the  school  and  routine,  and  the  utter 
one  sidedness  peculiar  to  men  of  modern  science  in  some  of 
the  highest  positions. 

The  opening  words  of  Leduc  (1.  c.,  p.  299)  are: 

"Taking  as  basis  O  =  16,  I  have  admitted  for  the  atomic 
i(  weight  of  carbon,  C  =  12.004,  which  seems  to  be  within 
11  i  oo  0(0  according  to  the  experiments  of  Mr.  Van  der  Plaat 
"(Synthesis  of  C  02)." 

By  the  way,  this  V.  d.  P.  never  made  an  atomic  weight 
determination  of  true  carbon.  See  p.  105,  supra. 

The  last  paragraph  of  this  same  article  (1.  c.,  p.  301),  is: 

"As  to  sulphur,  the  experiments  of  Stass  (synthesis  of  the 
"  sulphide)  give  the  atomic  weight  32.056.  /  shall  adopt 
<c  this  number,  although  the  experiments  of  Dumas  lead  to 
"  31.986  and  those  of  Erdmann  and  Marchand  to  32.005. " 

Leduc  constantly  deprives  the  Hollander  of  the  terminal 
s  in  his  name,  and  as  constantly  attaches  it  to  that  of  Stas, 
so  as  to  make  it  Stass — a  very  unpleasantly  suggestive  one 
to  English  readers.  Stas  was  not  that  kind  of  an  animal, 
any  way. 


l68  ABSOLUTE   ATOMIC   WEIGHT. 

By  his  density  determinations,  Leduc  is  compelled  to 
take  N=  14.005. 

In  this  condition  Leduc  says  (1.  c.,  p.  300) : 

"  But,  according  to  Stass,  we  ought  to  have  N  =  14.044 
"  together  with  €1  =  35.457  and  Ag=  107.929.'* 

"  The  difference  of  our  two  numbers  is  enormous :  ^itf! 
"  I  have,  however,  succeeded  to  explain  this,  -without  putting 
"  in  doubt  the  excellency  universally  recognized  of  the  experi- 
"  ments  of  Stass. " 

This  "  success "  is  the  raising  of  the  atomic  weight  of 
chlorine  by  0.013  and  the  lowering  of  that  of  silver  as  much. 
Of  course,  that  will  not  affect  the  weight  of  silver  chloride. 

What  a  havoc  this  little  change  would  play  all  round  the 
mystic  circle  or  Stas'  values,  Leduc  has  not  the  remotest 
idea  of.  He  is  as  innocent  of  this  entire  subject  as  a  new 
born  babe.  That  makes  his  reconciliation  of  Stas  with 
truth  so  funny. 

As  stated,  we  suppose  that  in  the  physical  laboratory  of 
Prof.  Lippmann  measuring  and  weighing  of  gases  is  done 
accurately — although  the  understanding  of  the  rudiments  of 
general  chemistry  is  palpably  lacking. 

At  all  events,  the  weighings  of  Lord  RayJeigh  do  not 
need  any  confirmation,  so  far  as  we  are  concerned;  there- 
fore, I  was  much  in  doubt  whether  I  should  introduce  the 
weighings  of  Leduc  at  all. 

I  beg  again  to  state  that  it  is  merely  his  weight  of  a  liter 
of  pure  oxygen  and  pure  nitrogen  for  which  we  here  intro- 
duce Leduc  as  a  witness. 

But  an  experimentor  who  takes  data  so  readily,  though 
he  states  they  are  not  true,  makes  a  pitiful  witness  even  as 
to  his  statements  of  weight  and  measure. 

What  causes  or  compels  working  scientists  in  some  of 
the  great  laboratories  of  Paris  to  make  such  exhibitions  of 
either  lack  of  general  scientific  training  or  servile  obeisance 
to  authority? 

The  above  examples  are  really  the  most  disgraceful  exhi- 
bitions of  that  kind  I  have  ever  seen. 

In  the  words  of  Hamlet,  "  there  is  something  rotten  in 
the  State  of  Denmark." 


DETERMINATION    BY    CHEMICAL    MEANS.  169 

B.     THE  FOLLY  AND  FRAUD  OF  STAS  AND 
HIS  SCHOOL. 

Determination  by  Chemical  Means. 

The  atomic  weight  of  nitrogen,  established  upon  the 
density  determinations  of  Lord  Rayleigh,  is  14  exactly. 

This  result  is  confirmed  by  the  later  weighings  of  Leduc. 

Hence  the  true  atomic  weight  of  nitrogen  is  14  exactly. 

But  these  determinations  are  not  strictly  chemical  ones. 
The  Stasian  will  say  so  and  demand  such. 

We  have  already  given  a  most  exquisite  chemical  deter- 
mination of  the  atomic  weight  of  nitrogen,  according  to 
which  it  is  14  exactly;  the  actual  precision  being  as  high 
as  o.ooi. 

We  refer  to  the  Synthesis  of  thallium  nitrate  by 
Crookes,  having  now  the  perfectly  satisfactory  determina- 
tions by  Lepierre  of  Tl  =.  204. 

The  question  of  the  true  atomic  weight  of  nitrogen  is 
therefore  settled,  both  by  the  physical  (Lord  Rayleigh)  and 
by  the  chemical  (Crookes)  determinations. 

But  here  is  the  dominant  School  of  Stas.  It  has  put  off 
my  True  Atomic  Weights  of  1894,  with  extrapolation  (p.  71), 
foolish  impudence  (p.  56),  and  kindred  tricks  and  bluffs. 

I  shall,  therefore,  in  this  final  exposition,  neither  presume 
on  their  honor  nor  on  their  scientific  intelligence.  I  shall 
simply  handle  the  facts  in  the  interest  of  scientific  truth. 

I  shall  wield  the  facts  just  as  they  are,  and  treat  the 
Stasians  exactly  as  they  have  shown  they  must  be  treated. 

My  object  is  not  to  convince  them — for  I  am  sorry  to  say, 
that  most  of  them  really  do  not  seem  to  have  any  convic- 
tions, either  scientific  or  moral. 

Why  was  the  statement,  by  Lemoine,  in  the  Academy 
of  Sciences  of  Paris,  so  remarkable?  (See  p.  157.) 

Would  Lemoine  have  accentuated  the  character  of  Friedel 
in  the  manner  he  did,  if  such  a  character  were  the  rule  and 
not  the  exception  among  the  scientific  men  in  some  regions? 


I7O  STASIAN    FOLLY   AND    FRAUD. 

The  Stasians,  having  corrupted  science,  have  also  cor- 
rupted themselves.  I  have  the  facts  at  hand.  I  forbear. 

But  if  my  object  is  not  the  conversion  of  the  Stasian 
Chemists,  what  do  I  aim  at? 

I  direct  my  words  to  the  thousands  of  young  men  now 
studying  chemistry  in  Universities  and  Colleges  throughout 
the  world,  or  having  left  these  institutions  within  ten  years. 

These  are  the  Chemists  of  the  Ftiture,  and  it  is  above  all  to 
these  Chemists  of  the  Future  that  I  direct  my  words. 

At  the  same  time,  the  question  discussed  is  so  broad  in 
its  general  scientific  character,  that  I  have  tried  to  express  it 
so  as  to  be  understood  by  all  scientific  students  and  the 
scientific  public  generally. 

I  shall  treat  this  subject  in  three  chapters. 

First,  the  Challenge  of  Stas  will  be  considered,  as  made 
and  as  answered. 

Second,  the  Synthesis  of  Silver  Nitrate  will  be  thoroughly 
examined  into,  and  the  absolute  lack  of  concordance  of  its 
results  will  be  shown. 

Third,  the  reaction  between  Silver  Nitrate  and  Potassium 
Chloride  will  be  critically  examined. 

This  will  really  end  the  scientific  discussion.  But  having 
been  compelled  to  waste  so  much  time  on  so  miserable  a 
subject,  we  are  all,  readers  as  well  as  writer,  entitled  to  a 
slight  gratification. 

We  shall  present  this  gratification  in  two  serio-comic 
historic  papers,  namely: 

ON     THE     DISCOVERY     OF     THE     CHANGE     OF     THE 

WEIGHT    OF    MATTER    by    chemical    combination    or 
decomposition;  and  lastly, 

HERESY  IN  THE  CHURCH  OF  STAS. 

With  these  two  historic  essays  showing  the  utter  rot- 
teness  of  Stasism,  we  shall  close  this  discussion,  and  proceed 
to  the  summing  up  of  the  case. 

I.     THE  CHALLENGE  OF  STAS. 

The  exact  atomic  weight  of  nitrogen  has  been  known  for 
forty  years,  we  are  constantly  told;  it  has  been  determined 


THE    CHALLENGE    OF    STAS.  171 

by  chemical  means  with  a  wonderful  degree  of  precision 
and  certainty  by  Jean-Servais  Stas.  See  my  True  Atomic 
Weights,  1894;  p.  33. 

It  is  14.041  in  1860;  14.044 in  1865;  14.055  in  1882 — accord- 
ing to  Stas  and  his  Dutch  Re-Calculator,  Van  der  Plaats 
(True  Atomic  Weights,  p.  34). 

It  is  14.041  according  to  his  Great  Official  American  Re- 
Calculator  Clarke  (edition  1897,  p.  71);  the  probable  error 
being  0.002 1  only. 

As  no  one  to-day  can  know  chemistry  without  being  able 
to  read  German  (until  1870  the  language  of  chemistry  was 
French,  for  till  then  chemistry  was  declared  to  be  a  French 
science*),  I  shall  quote  the  greatest  German  authority  on 
this  Atomic  Weight  in  the  learned  German : 

"Das  endgiiltige  Atomgewicht  des   Stickstoffs  ist  nach 
den  oben  berechneten  Untersuchungen  von  Stas  gleich 
N  =  14.0410  i  0.0037." 

See  Ostwald,  Physikalische  Chemie.     Bd.  I,  p.  sso;  1891. 

How  thoroughly  Professor  Ostwald  is  competent  for 
atomic  weight  calculations  and  how  fully  he  understands 
the  proper  use  of  the  method  of  the  least  squares  in  the  cal- 
culation of  the  probable  error  of  a  mean  atomic  weight,  I 
have  tried  to  show  pp.  42-46  of  my  True  Atomic  Weights, 
1894. 

Take  these  leading  authorities — differing  more  than  they 
ought  to,  if  the  work  of  Stas  were  what  it  is  proclaimed  to 
be — we  must  accept  N  =  14.04  as  the  value  agreed  upon  by 
these  authorities. 

Stas  himself  is  on  record  as  to  the  degree  of  certainty  of 
this  value.  He  has  put  his  statement  in  a  most  formidable 
mathematical  form.  He — evidently  by  some  mathematical 
friend,  probably  A.  Quetelet,  who  knew  as  little  of  chem- 

*Now,  under  the  leadership  of  Moissan,  young  French  Chemists  in 
the  great  National  Chemical  Laboratories  at  Paris  are  directed  to  take 
their  fundamental  chemical  data  from  the  "  Three  German  Chemists  " 
adopted  by  a  vote  of  the  German  Chemical  Society — and  the  said  young 
French  Chemists  thereby  actually  spoil  and  falsify  their  excellent  labora- 
tory work. 

This  is  the  "New  Era  of  Chemistry"  in  Paris.     See  p.  155,  also  p.  34. 


172  STASIAN    FOLLY   AND    FRAUD. 

istry  as  Stas  knew  of  mathematics — has  quoted  the  precise 
transcendental  formula  giving  the  ii probability  y "  as  a 
function  of  the  "  error  *." 

Not  wishing  to  shine  with  mathematical  formulae,  I  shall 
not  copy  it  here ;  the  formula  is  printed  in  the  entire  quota- 
tion from  Stas  on  this  subject,  p.  33  of  my  True  Atomic 
Weights. 

Stas  gives  (also  by  the  aid  of  that  mathematical  friend, 
for  Stas  himself  could  neither  do  that,  nor  did  he  ever  learn 
to  understand  the  result  he  states),  the  probability  calcu- 
lated from  that  formula  for  the  different  values  14.040, 
14.030,  14.020,  14.010  and  finally  14.000. 

He  declares  that  the  value  14.040  (instead  of  his  14.044) 
is  possible ,  its  chances  being  3  in  10;  that  is,  its  probability 
was  found  to  be  0.31278.  Of  these  five  decimals,  four  are 
transparent  moonshine.  See  p.  19. 

The  probability  of  N  being  14.000  is  stated  to  be 

y  =  o.o  .  .  .  .o  (370  ciphers)  879 
and  is  accordingly  declared  to  be  entirely  impossible. 

He  berates  chemists  for  using  14,  which  he  has  proved  to 
be  in  error  to  the  extent  of  *  3  \-^. 

See  complete  translation  on  p.  33  of  my  True  Atomic 
Weights  of  the  famous  passage  of  Stas  in  Aronstein's  Trans- 
lation, pp.  322-323,  and  the  original  reprinted  in  the  final 
Oeuvres  of  Stas,  vol.  I,  p.  731 ;  1894. 

Relying  on  this  mathematical  result,  Stas  finally  added 
to  his  paper  here  considered,  first  published  by  the  Belgian 
Academy  of  Sciences  in  the  35th  Volume  of  their  Memoirs, 
issued  in  1865,  the  famous  Challenge  to  the  Chemists  of  the 
World,  present  and  to  come.  See  Oeuvres  I,  p.  749;  also 
Aronstein's  Translation,  p.  347;  (published  Leipzig,  1867) 

This  challenge  Stas  repeated  in  his  last  work  on  Atomic 
Weights,  issued  from  1876  to  1881.  See  Oeuvres,  I,  p.  814; 
1894.  See  also,  True  Atomic  Weights,  p.  34. 

The  gist  of  this  challenge  is  the  request  to  repeat  his  syn- 
thesis of  silver  nitrate,  which  he,  therefore,  considered  the 
most  conclusive  of  all  his  determinations  of  the  atomic 
weight  of  nitrogen. 

*  Leduc  quite  recently  made  this  identical  discovery,  see  p.  168. 


THE    CHALLENGE    OF    STAS.  173 

Neither  his  challenge  of  1865,  nor  its  i(  Renouvelation  " 
in  1881,  has  ever  been  taken  up.  At  least,  no  chemist  has 
taken  the  trouble  to  repeat  this  work  of  Stas. 

I  venture  to  say  that  no  chemist  ever  will  repeat  it. 

The  challenge  is  not  a  demand  to  disprove  the  value 
N=  14.04  claimed  to  be  true;  for  that  value  has  been 
demonstrated  to  be  false,  at  least  by  myself  in  my  True 
Atomic  Weights  of  1894.  Some  of  the  most  eminent  chem- 
ists of  the  time  have  admitted  this,  my  demonstration,  to  be 
final.  Here  I  may  only  mention  the  work  of  Schiitzenberger 
in  the  Actualites  of  1896  already  referred  to,  and  in  his 
posthumous  General  Chemistry,  Paris,  1898,  pp.  143-152. 

That  the  method  of  procedure  of  Stas  cannot  give  true 
values  has  also  been  pointed  out  by  Schiitzenberger  on  the 
ground  of  his  own  experiments;  see  close  of  his  paper, 
Actuality's,  Paris,  1896,  p.  16. 

We  shall  here  once  more  prove  it,  this  time  by  Stas  him- 
self, that  his  method  of  determining  the  atomic  weight  of 
nitrogen  by  his  so-called  syntheses  of  silver  nitrate  is  a  most 
remarkable  mixture  of  chemical  folly  and  error,  or  rather 
fraud. 

Let  us  take  the  weighings  of  Stas  as  published  by  himself, 
and  as  so  frequently  republished  by  his  numerous  Re-Calcu- 
lators (see  Footnote,  p.  75),  all  fully  represented  in  my 
"  True  Atomic  Weights,'*  1894,  from  page  40  to  69. 

Let  us  plot  the  results  of  Stas  for  the  atomic  weight  of 
nitrogen  as  ordinates  to  the  amount  of  silver  used  as  abscisses. 

We  get  in  this  way,  tivo  curves,  one  for  the  dried  silver 
nitrate,  the  other  for  the  fused  silver  nitrate,  and  accordingly 
two  entire  SERIES  of  different  atomic  weights,  really  an 
infinite  number  of  atomic  weights  of  nitrogen,  in  two  great 
sets,  the  larger  for  the  dried,  and  the  smaller  for  the  fused 
silver  nitrate.  See  Plate  III,  facing  page  161  of  my  True 
Atomic  Weights,  1894,  constructed  from  data  printed  on 
page  164. 

On  account  of  the  great  importance  of  this  subject,  I 
will  here  give  a  brief  summary  of  the  essential  data  of  Stas, 
and  present  a  new  drawing  carried  to  600  grammes  and  free 


174  STASIAN    FOLLY   AND    FRAUD. 

from  the  other  curves  relating  to  other  work  of  Stas — also 
drawn  on  a  smaller  scale  for  the  silver  used.     See  Plate  II. 

We  shall,  once  more,  give  all  the  essential  data,  exactly 
as  given  by  Stas;  gross  actual  errors  of  Stas  we  shall  point 
out,  as  we  did  in  our  True  Atomic  Weights  of  1894.  But 
we  shall  be  as  brief  as  possible — referring  for  additional 
details  to  the  above  work  of  ours,  published  in  1894. 

Syntheses  of  Silver  Nitrate  by  Stas. 

Stas  made  ten  syntheses  of  silver  nitrate  from  pure  silver; 
we  designate  them  Nos.  i  to  10,  in  the  order  in  which  Stas 
actually  made  them.  The  results  were  published  by  him  in 
his  Recherches  of  1860  (Nos.  i  to  8),  and  in  his  Nouvelles 
Recherches  of  1865  (our  Nos.  9  and  10). 

The  full  and  complete  record  is  reprinted  in  his  Oeuvres, 
T.  I.,  1894;  for  the  first  series,  Nos.  i  to  8,  on  pages  342  to 
346;  for  his  second  series,  Nos.  9,  10,  on  pages  717  to  725. 

See  also  my  True  Atomic  Weights,  pp.  75  to  88;  1894; 
also  Clarke,  Constants,  1897,  p.  63. 

Our  re-calculation  of  the  analytical  ratios  gives  essenti- 
ally the  same  results  as  all  others  have  found,  and  as  given 
by  Stas  himself;  the  analytical  ratio  is  the  weight  of  the 
nitrate  divided  by  that  of  the  metal. 

In  other  words,  the  analytical  ratio  expresses  the  amount 
of  silver  nitrate  per  unit  of  "weight  of  silver  used. 

It  cannot  be  expected  that  we  should  again  reprint  these 
ratios  here ;  they  have  been  printed  often  enough,  even  by 
ourselves  (True  Atomic  Weights,  p.  77,  p.  81)  and  repre- 
sented graphically  on  plate  I  facing  this  last  page  just 
referred  to. 

As  to  these  data,  we  must  make  the  following  brief 
annotations: 

No.  7  is  excluded  by  Stas  himself;  hence  we  cannot  make 
use  of  it  here.  He  claims  to  have  lost  some  material.  We 
cannot  go  back  of  his  statement  of  fact.  We  accept  it  as  a 
matter  of  course. 

From  all  determinations,  Nos.  i  to  5  and  7,  we  have  found 
that  the  reduction  to  vacuum  amounted  to  21  milligrammes 


THE    CHALLENGE    OF    STAS.  175 

per  hectogramme  of  silver  used  in  the  first  series.  True 
Atomic  Weights,  pp.  82-83. 

The  readers  of  any  mathematical  sense  will  understand 
and  appreciate  this  very  easy  and  compact  way  of  procedure, 
as  it  were  en-bloc;  and  they  will  also  be  astonished  that  this 
method  has  not  been  used  by  our  modern  chemists. 

How  crude  the  methods  in  use  actually  are,  passes  belief; 
we  may,  for  example,  point  to  the  delightful  formulae  used 
at  the  great  Laboratory  of  the  University  of  Pennsylvania, 
see  page  16  of  the  Thesis  for  Ph.  D.  by  Willet  Lepley 
Hardin,  1896. 

If  no  blunder  is  made  in  the  use  of  such  a  set  of 
formulas,  it  surely  is  no  fault  of  the  said  formulae. 

For  No.  8,  Stas  allows  30  mgr.  only,  while  this  rule  would 
give  42  mgr.  Hence  the  values  of  Stas  for  No.  8,  are  placed 
too  low.  We  have  not  changed  them,  but  must  insist  that 
this  error  be  kept  in  mind,  when  the  final  curves  shall  be 
considered  in  detail.  The  error  amounts  to  40  per  cent  on  the 
reduction  to  vacuum. 

There  can  be  no  question  about  this  very  grave  error  in 
the  work  of  Stas.  We  dare  not  overlook  it.  To  correct  for 
buoyancy  in  this  'way  is  to  falsify  the  record  of  experiment.  It 
is  fraud. 

To  commit  an  error  of  forty  per  cent  on  so  simple  a 
calculation  as  the  reduction  to  vacuum,  is  in  effect  just  as 
bad  as  an  actual  falsification  of  the  experimental  data  of  Stas. 

His  famous  re -calculators,  from  Leipzig  to  Washington, 
have  failed  to  see  this  palpable  error;  their  spectacles  were 
of  so  deep  a  Stasian  haze  that  they  may  be  excused. 

But  we  must  remember  that  the  values  No.  8  are  recorded 
too  low  by  this  error  of  Stas. 

We  shall  simply  point  it  out  here,  because  for  200 
grammes  (No.  8),  we  have  determinations  Nos.  2,  3,  4,  5, 
sufficiently  nearby,  corresponding  to  about  150  and  300 
grammes  of  silver  used. 

But  the  case  is  very  different  for  Synthesis  No.  6,  this 
being  the  most  important,  involving  the  highest  amount  of 
silver  used,  namely,  400  grammes;  it  is  therefore  the  last 


176  STASIAN    FOLLY   AND    FRAUD. 


point  that  can  be  actually  determined  by  experiment,  in  our 
curves. 

For  405  grammes,  our  rule — deduced  from  Stas'  own 
work,  Nos.  i  to  5  and  7,  gives  only  84  milligrammes  as 
the  reduction  to  vacuum. 

The  actual  values  used  by  Stas,  for  both  the  dried  and  the 
fused  nitrate,  are  150  milligrammes.  Here  the  error  of  Stas 
in  calculation  amounts  to  180  per  cent. 

To  obtain  so  great  a  reduction  for  the  buoyancy  of  the 
air,  the  barometric  pressure  must  have  been  54  inches  for 
ordinary  temperatures,  or  the  temperature  200  degrees  below 
zero  for  ordinary  barometric  pressure. 

I  suppose  that  even  the  blind  admirers  of  Stas  do  not 
know  of  any  cave  or  pit  in  the  Laboratory  of  Stas  four 
thousand  meters  deep — a  sort  of  an  inverted  Mount  Blanc; 
nor  will  they  pretend  that  Stas  could  have  weighed  his 
wondrous  synthetic  silver  nitrate  at  a  temperature  uncom- 
fortably near  the  absolute  zero. 

There  is  nothing  to  do  but  to  admit  the  error  of  calcula- 
tion committed  by  Stas.  It  is  palpable. 

Such  errors  were  never  committed  by  Berzelius — for  he 
properly  looked  upon  this  whole  thing  as  a  folly,  as  a 
straining  at  gnats  while  swallowing  camels.  That  even  the 
greatest  analyst  of  modern  times,  as  which  we  are  demanded 
to  consider  Stas,  in  one  case  out  of  eight,  puffed  up  the 
gnat  to  a  good  sized  calf  of  a  camel  (No.  8),  and  in  the 
other  made  quite  a  full  grown  camel  out  of  it  (No.  6), 
committing  an  error  of  66  milligrammes  in  the  weight 
recorded  and  reprinted  by  his  admiring  re-calculators,  is 
quite  astonishing. 

This  error,  at  the  end  of  our  curves,  we  cannot  permit  to 
remain.  We  shall  mark  on  our  diagrams  the  points  (dry  and 
fused)  for  No.  6  exactly,  as  given  by  Stas  and  his  great  and 
careful  re-calculators ;  but  we  shall  mark  them  by  the  words 
" false"  or  "error"  and  add  the  correct  points  obtained 
by  the  correct  values  of  reduction,  which  points  we  shall 
mark  true  in  this  and  related  diagrams.  See  Plates  I,  II,  III. 

From  the  analytical  excess  observed,  we  calculate  in  our 
usual  way  the  atomic  weight,  here  of  nitrogen. 


PLATE    II. 

Atomic    Weight    of    N  itTOtje  TV  Tciu.lt..  n^ 


i 1 


1 


STAS:     ATOMIC  WEIGHT  OF  NITROGEN*. 

If  Stas'  work  were  true,  this  plate  would   show  one  single  straight 
line,  parallel  to  the  longest  dimension  of  the  cut.     See  pp.   174-182. 


THE    CHALLENGE    OF    STAS.  177 

These  calculated  values  therefore  are  based  upon  O  =  16 
and  Ag  =  108,  our  standard  values. 

Thus  the  absolute  values  for  N  may  not  suit  the  Stasians; 
but  I  do  hope  they  will  understand,  that  for  any  value  of 
silver,  near  108,  any  changes  in  the  resulting  calculated 
value  of  N  will  vary  in  the  same  way,  independent  of  the 
precise  value  of  the  atomic  weight  of  silver  taken. 

Besides,  I  already  here  promise  them  to  use  the  most 
Stasian  of  all  data  "  next  time,"  namely  those  of  Frank 
Wigglesworth  Clarke. 

I  am  afraid,  that  the  Stasians,  after  reading  both  papers, 
will  hardly  know  which  values  they  like  the  best,  those 
obtained  by  our  own  standard,  or  those  calculated  by  means 
of  the  Stasian  auxiliary  values  for  O  and  Ag,  furnished  by 
Clarke. 

At  any  rate,  108  is  the  true  atomic  weight  of  silver  as  we 
shall  prove,  and  107.92  is  false,  as  are  all  the  values  of  Stas. 
But  I  here  merely  wish  to  call  attention  to  the  fact  that  the 
difference  of  0.08  on  108  can  have  no  influence  whatever  on 
the  enormous  systematic  variations  ive  shall  find  in  the  atomic 
•weight  of  nitrogen,  resulting  from  the  syntheses  of  silver 
nitrate  made  by  Stas. 

The  following  table  (copied  from  our  True  Atomic 
Weights,  p.  164)  gives  these  results : 

Stas  Syntheses  of  Silver  Nitrate. 

Silver,  Atomic  Weight  of  Nitrogen. 

No.  Grammes.  Dried.  Fused. 

i  77  14.092  14.070 

2,  3  150  14.097  14.078 

8  200  14.087  14.067 

4,  5  300  14.076  14.069 

6        True     405  14.050  14.041 

6        False     405  14.069  14.060 

We  have  here  combined  the  neighboring  2,  3  and  4,  5; 

but  on  our  diagram  they  are  given  separately. 

These  values  have  been  carefully  entered  on  large  scale 
diagram,  from  which  we  have  had  a  photographic  reduction 
made,  see  Plate  II.  On  this  diagram  we  have  also  inserted 


178  STASIAN    FOLLY   AND    FRAUD. 

the  values  of  Marignac  (fused  nitrate),  forming  approxi- 
mately a  straight  line  running  from  the  origin  O  to  P.  We 
shall  not  here  enter  upon  details,  as  we  wish  exclusively  to 
consider  the  work  of  Stas. 

In  examining  this  very  instructive  diagram,  in  which  the 
ordinates  are  the  atomic  weight  (excess  above  14)  of  nitro- 
gen, and  the  abscissae  are  the  amount  of  silver  used  (in 
grammes)  and  remembering  that  all  determinations  are 
marked  by  the  proper  number,  we  notice : 

I.  The  determination  No.  7  rejected  by  Stas  is  far  below 
the  value  for  200  grammes;  hence  his  reason  for  rejecting  it 
must  have  been  a  good  one. 

II.  The  "  dried  "  nitrate  cannot  have  been  of  quite  uni- 
form character.     We  see  "  No.  2  dried  "  much  higher  above 
fused,  than  No.  3;  this  error  of  Stas  we   have  practically 
eliminated  by  taking  the  mean  of  these  two  determinations, 
which  is  marked  2,  3  on  the  diagram. 

The  difference  in  No.  3  is  seen  to  be  only  one-fourth  of 
that  in  No.  2,  between  the  dried  and  the  fused  nitrate.  This 
constitutes  an  error  of  300%  for  No.  2  as  compared  to  No.  3. 

III.  Another  such  greatly  differing  "drying"  we  see  in 
Nos.  8  and  the  two   determinations   4,  5.     These   last  two 
were  both  made  with  300  grammes  of  silver,  and  the  results 
were  almost  identical. 

In  this  point,  4,  5,  we  notice  the  difference  between 
"dried"  and  "fused"  less  than  half  what  it  is  for  No.  8. 
An  error  of  100%  for  No.  8,  as  compared  to  Nos.  4,  5. 

IV.  We  furthermore  notice  that  this  No.  8  lies  compar- 
atively Zoiv,  but  we  expected   that,  because  we  have  above 
shown,  that  Stas  committed  the  grave  error  of  adding  30 
milligrammes  only,  instead  of  the  true  value  of  42  milli- 
grammes for   reduction   to  vacuum — an   error  of  12  milli- 
grammes. 

If  I  had  "  corrected »'  also  this  error  of  Stas,  the  true 
value  No.  8  fused  would  have  fallen  almost  exactly  on  the 
full  drawn  curve. 

V.  The  great  error  of  Stas  in  No.  6  ive  have  sho~vn  to 
amount  to   66   milligrammes^  too    high,    in    this    case.     The 


THE    CHALLENGE   OF    STAS.  179 

points  determined  by  the  data  of  Stas  in  error  lie  away  above 
our  curves.  Our  true  values  lie  exactly  on  the  curves.  We 
have  supposed  that  Stas,  as  a  matter  of  fact,  was  not  work- 
ing in  a  pit  4,000  yards  deep,  nor  in  a  room  the  temperature 
of  which  reaches  within  70  degrees  of  the  absolute  zero;  but 
that  temperature  and  pressure  at  No.  6  were  about  the 
average  of  what  they  were  for  Nos.  i,  2,  3,  4,  5  and  7. 

VI.  Of  course,  we  would  not  say  that  Stas  intentionally 
falsified  his  record  for  No.  6  and  No.  8;  but  all  the  same  it 
is  a  remarkable  fact,  that  by  getting  No.  6  "  high  "  and  No. 
8  "  low  "  his  values  got  very  much  nearer  into  line  than  they 
are  in  fact;  that  is,  by  the  curious  "mistake"  committed  in 
the  reduction  to  vacuum,  giving  in  No.  8  a  value  40%  low 
and  in  No.  6  a  value  iSofo  high,  the  false  results  given  by 
Stas  approach  more  nearly  a  common  mean,  than  they  do 
without  those  two  "  mistakes." 

That  none  of  the  eminent  and  honest  Re-Calculators 
detected  these  mistakes  of  Stas  is  perfectly  natural.  "  Blind 
followers  of  a  blind  guide "  are  not  expected  to  see  much. 

VII.  Taking  now  the   points— both  for  "dried"   and 
"  fused  "  nitrate,  marked  i  —  mean  2,  3  —  8,  raised  —  mean 
4,  5  —  true  6  —  we  can  draw  a  curve  through  each  of  these 
two  sets,  namely  (always  see  Plate  II)  : 

Curve  A  B  C  D  for  dried  silver  nitrate;  and 
Curve  E  F  G  H  for  fused  silver  nitrate. 

VIII.  The  total   range  of  actually   determined  values 
runs  from  6,  fused,  true,  14.041  or  14.04,  to  2,  3,  dried,  14.097 
or  14.10,  showing  a  total  range  of  0.06. 

IX.  But  the   range  actually   observed    is  still   greater, 
because  No.  2,   dried,   is    14.11,   making  the   entire   actual 
range  0.07. 

X.  Since  now  the  pretended  value  of  Stas  is  14.04,  the 
range  of  his  own  determinations  (say  only  0.06)  is  greater 
by  50%  at  least,  than  the  value  he  has  pretended  to  deter- 
mine, namely,  the  exact  excess  0.04  above  14. 

XI.  When  the  determinations  are  of  such  varying  kind, 
science  holds  that  no  determination  has  been  affected. 


l8o  STASIAN    FOLLY   AND    FRAUD. 

XII.  It  is  also  generally  known,  and  should  certainly  be 
known  by  all  who  pretend  to  be  experts  in  this  matter  of  the 
reductions  of  experimental  determinations,  that 

When  the  observed  values  for  a  constant  follow  a  definite 
cttrve,  there  are  systematic  errors  present,  and  the  arithmetical 
mean  of  the  observed  values  has  no  sense  at  all. 

The  constant  here  in  question  is  the  atomic  weight  of 
nitrogen — or  the  analytical  ratio  of  Stas. 

If  we  accept  the  famous  syntheses  of  silver  nitrate  by 
Stas,  to  be  exactly  true  as  reported  (and  corrected  for  pal- 
pable errors  in  No.  8  and  No.  6,  as  shown),  what  do  his 
actual  results  prove? 

XIII.  That  the  atomic  weight  of  nitrogen  is  a  function 
of  the  amount  of  silver  used  in  its  determination;  and 

XIV.  That  the  atomic  weight  of  nitrogen  is  higher  in 
dried  nitrate  than  in  fused  nitrate  of  silver. 

XV.  This  difference  between  what  we   may   briefly  call 
"dried"  and  "fused"    atoms   of  nitrogen   is  greatest  for 
about  150  grammes  of  silver  taken  by  Stas  for  a  determina- 
tion ;  and  that 

XVI.  This    difference,    for     150    grammes    of     silver, 
amounts  to  about  0.02,  which  is  fully  one-half  of  the  entire 
excess  0.04  claimed  by  Stas  for  N  above  14  exactly. 

XVII.  It  appears   also  very  plainly,   that  if  Stas  had 
continued  to  work  exactly  in  the  manner  as  he  did  (but  had 
kept  out  of  pits  4000  meters  deep,  and  stayed  away  from  his 
laboratory  when  it  got  200  degress  below  the  freezing  point) 
he  would  have  found  values  for  N  getting  less  and  less,  as 
he  used  more  and  more  silver;  he  would  also  have  found  the 
fused  and  the  dried  silver  nitrate  to  differ  less  and  less  in 
weight.     See  our  curves,  Plate  II. 

XVIII.  And  finally,  if  he  had  made  a  few  determinations 
with  550  to  580  grammes  of  silver,  he  would  have  obtained 
practically  the  same  weight  for  his  dried  and  fused  silver 
nitrate,  and 

XIX.  The  atomic  weight  of  nitrogen  would  have  been 
found  exactly 

N  =  14.000. 


THE    CHALLENGE   OF    STAS.  l8f 

XX.  Since  now  the  otherwise  exacting  Stasians  have 
not  yet  decided  which  atoms  of  nitrogen  are  the  true  ones, 
those  merely  "  dried"  or  the  lighter  "/used"  ones;* 

And  since  it  always  has  been  our  desire  to  help  the 
Stasians  out  of  their  holes  (even  if  four  thousand  meters 
deep)  ;  we  shall  suggest,  that 

they  use  360  grammes  of  silver^ 

follow  exactly  the  method  of  their  master  Stas;    and  will 
then  find  N  =  14  exactly. 

And  as  then  there  is  no  further  difference  of  opinion 
possible,  we  shall  beg  their  kind  permission  to  close  this  little 
chapter  on  the  challenge  of  Stas  to  the  chemists  of  the  world. 

Postscriptum.  I  am  sure  ordinary  wide-awake  readers, 
such  as  our  common  American  students,  who  have  not  worn 
out  the  seats  of  too  great  a  number  of  pants  at  school,  will 
have  taken  note  of  the  delectably  minute  (i probable  error" 
of  the  Stasian  value  for  nitrogen,  and  found  a  great  deal  of 
innocent  amusement  in  comparing  this  minute  probable 
error  with  the  colossal  range  of  the  values  found  ;  but  I  fear 
my  Stasian  readers  have  overlooked  this — and  hence  the 
necessity  for  this  postscript. 

The  probable  error,  according  to  Clarke  is  21,  according 
to  Ostwald  is  37  units  in  the  fourth  place ;  the  mean  is  29, 
that  is,  0.0029,  for  which  I  think  we  may  be  pardoned  to  put 
0.003  or  3  thousandths. 

The  actual  range  we  found  0.07,  which  is  fully  23  times 
the  probable  error. 

The  total  number  of  determinations  being  7  out  of  the  8 
made  (No.  7  excluded  by  Stas),  and  the  square  root  of  7 
being  2%,  very  nearly,  the  probable  error  of  the  mean, 

*  I  greatly  dislike  foot-notes,  as  well  as  crooked  things  generally. 

But  I  have  called  attention  to  the  private  letter  of  Stas  to  Van  der 
Plaats  on  this  subject  in  my  True  Atomic  Weights,  p.  86,  which  private 
letter  of  Stas  was  published  as  to  its  main  contents  by  Van  der  Plaats  in 
his  paper  in  the  Annales  de  Chimie,  VII,  p.  518;  1886,  as  I  stated  with 
special  reference  to  volume  and  page.  Also  Comptes  Rendus,  no, 
p.  1363 ;  1893. 

IP  Crookes'  editorial  of  1896  he  makes  it  appear  that  I  have  drawn 
into  print  a  private  letter  of  Stas!  It  is  really  difficult  to  find  words  to 
condemn  such  crooks! 


1 82  STASIAN    FOLLY  AND    FRAUD. 

3  thousandths,  will  give  us  for  the  probable  error  of  a  single 
determination  8  thousandths,  that  is  0.008. 

Since  the  mean  of  Stas  is  14.041,  half  of  all  observed 
values  should  lie  within  the  range  0.008  below  and  above  this 
mean,  that  is  between  14.033  and  14.049;  let  us  say,  between 
14.03  and  14.05.  See  bottom  p.  n,  and  pp.  16-17. 

For  the  " fused"  nitrogen  atoms  here  considered,  only 
No.  6  falls  within  this  limit — the  other  six  determinations 
are  far  above  it,  being  located  between  14.06  and  14.08. 

For  the  "dried  "  atoms,  a  similar  state  of  facts  would  result. 

But  why  will  common  laborants,  who  like  the  janitors 
of  a  chemical  laboratory,  know  of  no  chemistry  beyond  the 
mixing  of  liquids  and  the  ignition  of  solids,  with  more  or 
less  of  stink  and  fumes,  meddle  with  mathematical  processes 
they  do  not  understand? 

It  is  like  playing  with  new  firearms — they  may  find  them 
loaded  when  least  suspecting  such  a  thing. 

They  ought  to  be  more  careful,  hereafter. 

II.     THE  ATOMIC  WEIGHT  OF  NITROGEN  BY  CHEMICAL  MEANS. 

Really  it  is  not  necessary  to  enter  upon  the  purely  chem- 
ical determinations  of  the  atomic  weight  of  nitrogen,  after 
the  perfectly  unquestionable  results  obtained  by  density 
determinations  of  Lord  Rayleigh  and  the  preceding  little 
Note  on  Stas'  Syntheses  of  silver  nitrate  and  his  challenge. 

But  the  muddled  state  of  the  chemical  mind,  produced 
by  the  pretenses  of  Stas  and  diffused  by  the  high  chemical 
and  academic  endorsements  of  Stas,  which  have  made  the 
expression  of  any  doubt  about  the  Stas  values  a  heresy, 
compel  us  to  enter  upon  this  chemical  part  once  more. 

I  must  be  permitted  to  insist  that  a  demonstrated  fact, 
such  as  the  atomic  weight  of  nitrogen  by  density  determina- 
tions, is  to  be  received  as  such,  and  cannot  be  suppressed. 
It  must  be  accepted  as  a  finality. 

Anything  in  conflict  with  such  a  fact  proves  itself  to  be 
in  error.  If  the  atomic  weight  of  nitrogen  obtained  by 
strictly  chemical  means  differs  from  14,  we  can  only  look  for 
causes  of  error  in  these  methods  of  determinations. 

But  as  a  still  further  concession  to  the  deplorable  lack  of 


NITROGEN    BY   CHEMICAL    MEANS.  183 

a  real  scientific  spirit  in  the  chemical  mind  of  the  last  forty 
years,  when  it  was  befogged  by  absolute  faith  in  false  methods 
and  imaginary  precision,  combined  with  absolute  ignorance 
of  general  principles  of  scientific  reasoning,  induces  me  to 
take  up  the  determination  of  the  atomic  weight  of  nitrogen 
by  chemical  means  entirely  de  novo,  as  if  the  determination 
by  density  had  not  been  made,  nor  that  challenge  taken  up. 

And  finally,  as  some  of  the  would-be  critics  in  high 
station  may  not  be  able,  nor  even  willing,  to  overcome  the 
inertia  of  their  own  mind,  so  thoroughly  rooted  in  the  false 
doctrine,  as  it  was  in  an  earlier  period  in  phlogiston — I 
shall,  in  this  case,  resort  to  their  own  familiar  method  of 
dealing  with  the  atomic  weight  determinations,  singly  and 
directly,  however  much  inferior  that  method  is  in  scientific 
force  to  our  method  of  dealing  exclusively  with  the  imme- 
diate results  of  experiment  expressed  in  the  analytical  ratio. 

I  shall,  therefore,  in  this,  the  most  noted  case,  make  use 
of  the  old  method  of  procedure  by  comparing  directly  the 
atomic  weights  immediately  resulting  from  the  individual 
analytical  data  of  the  laboratory  work — "  de  la  Chimie  du 
Laboratoire."  See  p.  22. 

In  this  case  I  shall,  of  course,  follow  the  common 
practice  of  stating  my  own  calculations  with  the  usual 
degree  of  "  precision  "  of  three  decimals. 

If  I  should  not  follow  this  modern  humbug  and  fail  to 
give  the  customary  imaginary  decimals  resulting  by  carrying 
on  calculation  beyond  the  plainest  limits  of  precision  of 
the  experimental  determinations,  I  would,  of  course,  be 
denounced  by  the  dominant  school,  or  rather  by  the  infalli- 
ble church  of  the  false  prophet  Stas,  as  lacking  in  the  first 
essential  requirement  of  modern  exact  science. 

But  finally,  what  shall  be  the  auxiliary  data  for  these 
calculations?  Our  standard  atomic  weights  are,  in  this  case, 
out  of  the  question ;  for  the  fanatics  of  the  church  of  Stas 
would  in  toto  reject  all  results  based  upon  our  own  standards 
and  calculated  by  our  own  methods. 

We,  therefore,  must  take  the  data  of  Stas  and  his  school. 
We  shall  take  those  presented  with  the  show  of  highest 
precision,  and  claiming  the  highest  authority. 


184  STASIAN    FOLLY   AND    FRAUD. 

These  are  to-day  undoubtedly  those  of  the  Smithsonian 
Institution,  declared  to  be  the  most  probable  by  the  Secre- 
tary thereof,  published  in  fullest  form  at  the  expense  of  the 
Smithsonian  fund,  entrusted  to  the  American  Congress  for 
the  Increase  and  Diffusion  of  KNOWLEDGE  among  men  "per 
orbem,"  and  sent  out  as  registered  mail  matter  at  the 
expense  of  the  entire  American  people. 

These  values  are,  furthermore,  produced  in  the  scientific 
bureaus  maintained  at  Washington  by  the  taxes  put  upon  the 
American  people.  In  this  instance,  the  chief  responsible 
for  this  work,  is  the  Secretary  of  the  Interior,  under  whose 
control  the  Geological  Survey  of  the  United  States  is  placed 
by  law.  The  real  (ostensibly  the  only)  author  is  the  Chief 
Chemist  of  that  Survey,  Frank  Wigglesworth  Clarke. 

We  shall  then,  for  this  one  instance,  use  the  final  data 
proclaimed  by  the  authority  of  the  Smithsonian  Institution, 
as  elaborated  in  and  by  the  Department  of  the  Interior  in 
one  of  its  highest  scientific  bureaus,  and  as  they  are  blindly 
accepted  by  the  American  Chemical  Society,  and  made  use 
of  in  the  enormous  establishments  of  this  Government  in 
the  collection  of  imports,  in  the  Department  of  Agriculture 
and  the  numerous  Experiment  Stations  of  this  Department. 

These  very  data,  the  false  atomic  weights  of  Clarke  and 
the  Smithsonian  Institution,  are  now  being  officially  forced 
upon  the  Committee  revising  the  U.  S.  Pharmacopoeia  for 
adoption  as  standards  in  this  work. 

If  these  final  data,  used  in  all  these  government  estab- 
lishments of  a  supposed  scientific  or  technical  nature  are 
false,  then  all  chemical  analyses  made  in  these  institutions, 
which  are  supported  at  the  cost  of  many  millions  of  dollars 
annually  to  the  American  people,  w///,  as  a  matter  of  necessity 
be  falsified  by  these  false  data — for  even  the  best  made 
chemical  analysis  will  be  so  falsified  if  the  data  used  for 
their  reduction  by  calculation,  are  false. 

With  this  matter  thoroughly  understood,  I  shall  now 
proceed  to  the  work  of  testing  the  value  given  to  the  atomic 
weight  of  nitrogen  by  chemical  means,  according  to  the  com- 
mon method  of  calculating  this  atomic  weight  in  every  single 
analysis  or  determination  directly  from  the  analytical  ratio- 


NITROGEN    BY    CHEMICAL    MEANS.  185 

To  be  absolutely  beyond  reproach,  I  shall  take  this 
analytical  ratio  from  the  Smithsonian  tables  themselves, 
stating  the  page  of  the  "  Constants  of  Nature,"  of  1897, 
where  they  can  be  found. 

All  calculations  have  been  carefully  made  with  seven 
place  logarithms  (Schron's,  igth  edition,  Braunschweig, 
1881).  I  do  not  think  any  error  has  crept  in;  if  so,  I  shall 
gladly  accept  the  report  for  revision  and  proper  acknowl- 
edgement. 

The  limited  space,  because  of  limited  means  at  my 
disposal,  and  the  limited  time,  because  my  age,  does  not 
encourage  further  waste  of  my  time  on  the  greatest  scientific 
humbug  of  modern  days,  and  compels  me  to  limit  this  work 
to  the  tivo  most  famous — or  as  I  must  say,  scientifically 
infamous — determinations,  namely,  those  depending  on  the 
synthesis  of  silver  nitrate,  and  the  relation  of  the  silver 
nitrate  to  potassium  chloride. 

These  methods  are  generally  regarded  as  the  most  famous 
by  all ;  the  first  most  assuredly  is  always  represented  as  such, 
and  was  the  very  one  so  proclaimed  by  Stas  himself,  when 
he  challenged  the  chemists  of  the  world  in  the  sixties  and 
again  in  the  eighties.  The  second  is  next  in  standing. 

The  special  values,  required  in  our  reductions,  we  take, 
as  stated,  from  Clarke,  whose  absurd  unit  we  will  have  to 
use,  namely,  his  pretended  hydrogen  unit,  which  practically 
means  (1.  c.,  p.  33) 

O  =  15.879- 

The  value  is  pretended  to  be  affected  by  a  "  probable 
error"  of  only  0.0003. 

Clarke  (1.  c.,  p.  33)  says  that  the  above  value  "  will  be 
used  throughout  this  work,"  the  Constants  of  Nature,  1897. 
So  we  have  to  use  it  ourselves — for  this  once. 

May  the  God  of  Truth  pardon  me  for  basing  these  calcu- 
lations on  official  lies  and  scientific  fraud.  I  do  so  exclu- 
sively and  solely  to  thereby  prove  them  to  be  such  lies  and 
frauds,  in  order  to  destroy  them  and  to  blot  them  out  from 
the  face  of  Chemical  Science  which  they  have  disfigured 
and  disgraced  for  forty  long  years. 


l86  STASIAN   FOLLY   AND    FRAUD. 

a.    Synthesis  of  Silver  Nitrate. 

In  the  synthesis  of  silver  nitrate,  the  analytical  ratios  of 
experiment,  are  given  on  pages  62  and  63  of  the  Smithsonian 
Constants  of  Nature  of  1897.  See  also  my  True  Atomic 
Weights,  1894;  pp.  76-77. 

We  have  not  room  to  reprint  them,  but  give  the  resulting 
atomic  weights  under  the  heading  of  the  chemist  and  in 
exactly  the  same  order  as  in  the  work  referred  to;  hence 
absolute  identification  is  secured,  and  easy  reference  estab- 
lished. 

As  to  the  calculation  made,  according  to  common  prac- 
tice, the  following  words  will  suffice: 

The  analytical  ratio  a  of  each  determination  just  referred 
to,  expresses  the  quotient  Ag  Os  N  divided  by  Ag,  where  O 
has  the  value  above  stated  and  where 
Ag==  107.108 

(1  c.,  p.  70)  with  a  probable  error  of  0.003  only.     Accord- 
ingly, the  numerical  value  of  Ag  Os  is  154.745. 

Since,  now,  the  ratio  a  multiplied  by  Ag  equals  Ag  Os  N, 
it  follows  that  N  is  obtained  by  the  following  process: 

Multiply  the  numerical  observed  value  of  #,  by  the  given 
numerical  value  of  Ag,  substract,  from  this  product,  the 
above  numerical  value  of  Ag  Os  and  the  remainder  will  be 
the  numerical  value  of  N  due  to  the  determination  made. 

Atomic  Weight  of  Nitrogen  from  Syntheses  of  Silver  Nitrate. 
For  O  =  15.879  and  Ag  107.108. 


Chemist  : 

Penny. 

Marignac. 

Stas, 

,  First, 

Stas, 

Last. 

No. 

Dried. 

Fused. 

Dried. 

Fused. 

Dried. 

Fused. 

I 

I3-374 

I3-877 

J3-94I 

13.921 

13.944 

13.936 

2 

.882 

•843 

.960 

.929 

"943 

.928 

3 

.904 

.877 

•933 

•925 

4 

.885 

.846 

.922 

.918 

5 

.874 

.892 

.926 

.917 

6 

.901 

.918 

.900 

8 

•936 

.906 

Mean 

13-887 

13.867 

13-934 

13-919 

!3-944 

I3.932 

[Stas,  No.  6,  above    is     \ 
false;  true,                   J 

.899 

.890 

See  further  on.] 

SYNTHESIS    SILVER   NITRATE.  187 

This  little  table  contains  the  exact  atomic  weight  of 
nitrogen,  as  it  results  from  each  single  determination  made 
by  reducing  that  determination  in  the  common  way  by 
means  of  the  final  values  of  Clarke  for  the  auxiliary  elements 
O  and  Ag.  All  determinations  made  are  taken,  exactly  as 
recorded  by  their  analytical  ratios  on  pages  62  and  63  of  the 
work  of  Clarke  of  1897. 

Although  modern  chemists  do  not  look  at  facts  observed, 
but  only  at  means,  and  then  take  these  means  as  facts,  they 
will  please  not  do  so  in  this  particular  case,  but  keep  each 
real  fact  distinctly  in  view  by  itself. 

And  as  the  common  custom  of  leaving  numbers  in  a 
column,  does  not  give  the  eye  a  fair  chance  to  see  how  far 
these  values  agree — and  thus  the  mouth  and  the  pen  may, 
inadvertently  of  course,  proclaim  as  facts  what  is  merely  error 
or  vain  imagination,  we  shall  make  sure  to  avoid  such  an 
unhappy  result. 

To  avoid  such  a  deplorable  occurrence  of  filling  the 
record  of  science,  and  then  the  world,  with  unmitigated 
falsehoods  and  errors,  we  have  taken  the  trouble  to  assist 
the  eye  of  the  mind  by  a  simple  use  of  the  eye  of  the  head, 
through  plotting  the  above  data. 

In  the  original  drawing,  the  hundredth  of  the  unit  of 
atomic  weight  was  represented  by  one  inch,  the  thousandth 
was,  therefore,  represented  by  the  tenth  of  an  inch,  securing 
absolute  correctness  to  the  third  decimal — in  this  drawing, 
of  which  a  photo-reduction  is  printed  on  the  lower  half  of 
Plate  I. 

In  order  to  keep  the  individual  series  properly  apart, 
each  series  was  laid  down  on  its  own  straight  line,  deter- 
mined in  place  by  the  mean  value  of  that  series. 

This  somewhat  new  method  of  graphical  representation 
gives  a  faithful  and  perfectly  clear  picture  of  all  the  facts: 
the  individual  observations  as  abscissae  on  lines  determined 
in  place  by  their  means  as  ordinates. 

As  a  matter  of  course,  the  locus  of  the  means  becomes  a 
line  inclined  under  45  degrees. 

The  results  from  dried  silver  nitrate  are  represented  by 
open  circles,  those  from  fused  silver  nitrate  by  black  circles. 


l88  STASIAN    FOLLY   AND    FRAUD. 

It  is  evident,  from  the  diagram,  that  these  two  conditions 
are  thoroughly  distinct;  for  the  "  dried  "  nitrate  the  atomic 
weight  is  invariably  almost  two  hundredths  higher  than  for 
the  fused  nitrate. 

This  is  true  for  Marignac  and  Penny  as  well  as  for  Stas. 

This  diagram  alone  must  suffice  to  condemn  the  position 
of  Stas  on  this  question,  as  to  which  silver  nitrate  is  the  true 
one,  the  dried  or  the  fused  ? 

Stas  and  his  school  have  left  the  question  practically 
open.  When  confronting  such  contrast,  they  hide  it  under 
the  pretention  that  it  is  of  minor  importance,  insignificant; 
but  in  the  next  breath  and  on  the  next  page,  they  claim  an 
accuracy  to  the  very  last  decimal! 

This  fooling  the  chemical  authorities  and  through  them 
the  entire  chemical  world,  has  been  carried  on  long  enough. 
It  is  worthy  of  the  mountebank,  but  not  becoming  the 
scientist,  least  of  all  when  he  proclaims  the  great  precision 
of  exact  science,  and  challenges  the  chemists  of  the  world, 
as  Stas  has  done  twice. 

Here,  in  this  our  diagram,  printed  from  a  photographic 
reduction  of  our  large  scale  drawing,  all  the  actual  facts 
observed  are  represented  in  space  to  an  exact  scale. 

First  of  all,  every  one  must  admit,  that  the  vaunted  con- 
cordance of  the  chemical  determinations  of  Stas  does  not  exist, 
is  not  a  fact,  but  merely  a  boastful  pretense. 

To  say  that  Penny  and  Marignac  differed,  and  that  their 
work  can  not  be  considered  in  connection  with  that  of  Stas, 
is  making  an  assertion  that  is  false  in  fact,  and  when  repeated 
after  this  exposition  will  become  a  wilful  falsehood. 

The  fact  is  palpably  evident  on  our  diagram,  Plate  I,  that 
Stas  i(  dried"  differsy>'0;#  Stas  " fused  "  exactly  as  badly  as 
Penny  u  dried '"  from  Marignac  " fused. ," 

It  is  also  palpably  evident,  that  Stas,  "  last  series  "  (Nos. 
9,  10),  differ  still  more  from  his  first  or  older  series,  (Nos. 
1-8;  7  he  withdrew),  in  a  direction  to  get  away  from  the 
older  chemists,  Penny  and  Marignac. 

Any  thoroughly  unbiased  mind  must  take  this  as  an  evi- 
dence of  intention  on  the  part  of  Stas. 

He  undertook  the  last  series  to  prove  simple  relations  of 


SYNTHESIS    SILVER   NITRATE.  189 

atomic  weights  to  be  wrong — and  he  pushed  the  value  of 
nitrogen  still  higher  up. 

These  differences  are  not  insignificant,  for  the  Stasians 
depend  upon  the  values  of  the  thousandths  in  the  claim  for 
exactness;  they  cannot  drop  this  when  confronted  with 
greater  discrepancies  between  Stas'  own  results  mutually, 
than  between  the  values  of  Marignac  and  Penny. 

The  entire  range  of  the  individual  determinations 
amounts  to  12  hundredths,  or  0.12,  on  the  atomic  weight  of 
nitrogen ;  that  is,  almost  ONE  per  cent! 

The  work  of  Stas  all  lies  on  one  side — the  work  of  the 
other  chemists  all  lies  on  the  other  side. 

This  diagram  shows  with  absolute  evidence  that  the  work 
of  Stas  is  in  no  way  more  reliable  than  that  of  the  other 
chemists. 

If  they  erred  to  one  side,  Stas  erred  as  much  on  the  other 
side! 

The  means  between  Marignac  and  Penny  differ  palpably 
no  more  than  the  means  between  Stas'  first  and  last  series. 

Marignac  fused  is 0.02  below  Penny  dried;  but  Stas  fused, 
first  series,  is  0.025  below  Stas  dried,  last  series. 

The  school  of  Stas  has  followed  the  example  of  its 
founder  to  the  letter;  it  has  descried  the  work  of  the  older 
chemists  as  inferior  in  exactness,  therefore,  practically 
worthless;  it  has  denounced  the  ideas  and  determinations  of 
other  chemists  as  ridiculous  imaginations  and  chimerical. 
See  pp.  78-79;  also  p.  99. 

Further,  as  to  the  pretended  higher  concordance  of  the 
individual  determinations  of  Stas  as  compared  to  those  of 
Marignac  and  Penny,  our  diagram  representing  all  the  facts 
equally  and  to  exactly  the  same  scale,  shows  this  boasted 
higher  concordance  in  Stas  work  is  also  nothing  but  a  sham 
and  a  pretense. 

The  fact  is  presented  in  our  diagram;  the  divergence 
increases,  from  an  approximate  center,  in  both  directions  I 

Stas  "  fused"  atoms  of  nitrogen  differed  less  than  his 
"  dried  "  atoms,  the  first  being  placed  nearer  that  center;  so 
did  the  "  dried  "  atoms  of  Penny  differ  less  than  the  "  fused  " 
atoms  of  Marignac. 


190  STASIAN    FOLLY    AND    FRAUD. 


The  general  fact  here  brought  out  is  that  the  further  the 
work,  not  in  itself  admitting  of  exact  determination,  is 
pushed  beyond  its  true  value,  in  order  to  secure  concordance, 
the  greater  will  be  the  constant  error. 

By  the  lines  A  B  and  C  D  (always  lower  half  of  Plate  I) 
limiting  the  Stas  values,  we  also  include  all  those  of 
Marignac,  for  the  fused  nitrate. 

In  the  same  way,  the  dotted  lines  marked  with  the 
accented  letters  include  all  determinations  on  dried  nitrate, 
whether  made  by  Penny  or  by  Stas. 

The  true  mean  of  the  determinations  for  c(  dried  "  atoms 
of  nitrogen  is  in  N',  taking  all  determinations  made.  Its 
value  is  13.906. 

The  true  mean  of  all  determinations  for  (( fused"  atoms 
of  nitrogen  is  at  N,  taking  all  determinations.  Its  value  is 
evidently  13.894. 

It  is  absurd  to  avoid  a  decision  as  to  which  of  these 
values  should  be  considered  the  most  reliable. 

The  "  drying"  did  not  affect  the  "  nitrate  "  we  are  made 
to  understand.  Hence,  the  "fused  nitrate"*"1  is  the  one 
alone  to  be  considered. 

But  what  is  the  value  of  this  N  =  13.894  in  the  ridiculous 
units  of  Clarke,  which  we  here  are  condemned  to  use? 

Dividing  this  value  by  14,  we  obtain  the  quotient  0.9924. 

Dividing  Clarke's  assumed  value  of  oxygen,  in  which  all 
values  are  de  facto  expressed,  namely  15.879,  by  16  we  obtain 
the  quotient  0.9926.  This  is  practically  the  same. 

The  mean  of  both  quotients  is  0.9925 ;  in  other  words, 
the  most  reliable  mean  value  of  all  determinations  on  fused 
nitrate  of  silver  give  for  N  a  value  exactly  \%  of  that  of 
oxygen. 

The  mean  N'  for  the  dried  silver  nitrate  is  about  the 
constant  value  too  high,  and  would  upon  drying  have  come 
down  to  about  N.  The  dotted  lines  on  our  diagram  would 
then  about  coincide  with  the  full  drawn  lines  A  B,  C  D 
passing  through  the  heavily  marked  point  N. 

Hence,  taking  all  determinations,  considering  all  about 
equally  well  made,  supposing  that  Marignac  and  Penny  were 
good  chemists  as  well  as  Stas,  possibly  less  biased;  and 


NITRATE    CHLORIDE    RATIO.  191 

allowing  for  a  proper  loss  of  the  dried,  so  as  to  take  the  fused 
as  the  true  condition  of  stiver  nitrate,  the  existing  chemical 
determinations  give  for  the  atomic  weight  of  nitrogen, 
practically  exactly  the  {$th  of  the  value  of  the  atomic  weight 
of  oxygen  used  in  the  reduction. 

Hence,  the  atomic  weight  of  nitrogen,  in  the  common 
way  of  reduction,  taking  all  determinations,  is  |$  of  that 
of  oxygen. 

But  we  know,  that  the  silver  nitrate  is  not,  even  when 
fused,  fit  for  accurate  atomic  weight  determinations. 
Indeed,  the  atomic  weight  of  silver  used  above,  namely, 
107.108  when  divided  by  108  gives  the  quotient  0.9918  which 
is  about  7  ten -thousandths  below  the  one  resulting  from 
both  N  and  O  above. 

This  shows  that  in  these  syntheses  the  error  has  been 
thrown  on  the  atomic  weight  of  silver,  by  Clarke  and  by  Stas. 

As  to  the  determination  No.  6  of  Stas,  the  diagram  shows 
the  false  values  given  by  Stas  himself,  and  also  the  true  ones 
obtained  by  us  in  reducing  the  actual  weighings  exactly  as 
demanded  by  the  real  conditions  prevailing  and  manifest  in 
the  other  determinations.  That  is,  I  do  not  believe  that  Stas 
made  determination  No.  6  at  the  bottom  of  a  pit  4000  meters 
deep,  nor  in  a  room  cooled  200  degrees  centigrade  below  the 
freezing  point  of  water. 

b.    The  Silver  Nitrate  and  Potassium  Chloride  Ratio. 

This  series  of  determinations  is  contained  in  the  Recher- 
ches  in  the  Bulletin  of  the  Belgian  Academy  for  1860,  pp. 
290-293,  and  in  Aronstein's  Translation,  pp.  306-308;  it  is 
reprinted  in  the  first  volume  of  the  Works  of  STAS,  issued 
1894,  on  pp.  379-381. 

By  Clarke  (1897),  the  analytical  ratios  are  given  on  page 
65,  and  the  final  results  for  the  atomic  weight  of  nitrogen 
on  pp.  70-71.  We  shall  here  again  refer  to  Clarke  for  the 
analytical  ratios,  and  take  his  atomic  weights  for  Ag,  O, 
Ka  and  Cl  for  our  calculations,  exactly  as  we  did  for  the 
synthesis  of  silver  nitrate. 


192  STASIAN    FOLLY   AND    FRAUD. 

The  data  used  are  the  same  values  for  O,  Ag,  as  before, 
to  which  now  must  be  added,  from  p.  70  or  any  other 

Ka  =  38.817  C1=35.I79 

giving  us  KaCl  =  73.996. 

The  analytical  ratio  a,  recorded  on  p.  65,  as  observed, 
gives  the  corresponding  atomic  weight  of  silver  nitrate  by 
dividing  the  ratio  into  the  above  73.996;  from  which  quotient 
we,  as  before,  subtract  the  value  of  Ag  Oa  =  154.745  to 
obtain  the  value  of  N  due  to  the  analytical  ratio  found  by 
the  chemist. 

Value  of  N  from  Ag  Nitrate  to  Ka  Chloride. 

Chemist :    Marignac  Stas  I.  Stas  II.  Stas  III. 

No.  i  14.057  13.895  13.945  13.834 

2  14.011  .907  .930  .895 

3  14.014  .907  .903  .868 

4  13.924  *    .911 

5  !3-899 

6  13-926 

Mean  13-972  13-905  !3-927  13.866 

These  actual  results  have  also  been  plotted  most  care- 
fully to  the  same  scale  used  for  the  nitrate,  namely,  o.oi  to 
the  inch;  the  reduced  photo-engraving  is  printed  on 
Plate  III. 

We  note  again  some  very  striking  facts  by  mere  inspec- 
tion. 

First,  we  see  that  the  concordance  diminishes,  as  before, 
in  both  directions  from  some  central  value,  near  the  heavy 
circle  marked  N  on  the  line  of  means. 

One  of  the  most  remarkable  facts  is  readily  recognized 
by  comparing  the  graphics  for  the  three  series  of  Stas. 

The  first  series  is  the  most  compact,  the  least  divergent; 
the  other  two  are  less  concordant. 

Of  these  the  second  lies  decidedly  high,  the  third  decid- 
edly low. 

In  the  original  record  of  Stas  (1.  c.,  p.  291),  we  learn  that 
Series  I  was  made  with  silver  nitrate,  many  times  recrys- 
tallized,  and  originally  prepared  from  pure  silver. 


PLATE    III. 


STAS:     ATOMIC  WEIGHT  OF  NITROGEN. 

Tf  Stas'  work  were  true,  all  dots  would   he  grouped  close  together. 
See  pp.  191-198. 


PLATE    III. 


STAS:     ATOMIC  WEIGHT  OF  NITROGEN. 

If  Stas'  work  were  true,  all  dots  would   he  grouped  close  together. 
See  pp.  191-198. 


NITRATE    CHLORIDE   RATIO.  193 

This,  therefore,  appears  to  have  been  the  purest  silver 
nitrate  used  by  him. 

The  second  series  was  made  from  the  material  used  in 
No.  6  of  the  syntheses — that  is,  which  must  have  been  4000 
meters  deep  or  200  degrees  below  freezing  point — conditions 
which  might  have  affected  it.  At  any  rate,  it  yielded  high 
values  for  N. 

The  third  series  was  made  by  dissolving  a  silver  deposit 
obtained  by  the  electrolysis  of  silver  cyanide  in  potassium 
cyanide. 

The  values  of  Marignac  are  above  all  those  of  Stas,  and 
less  concordant — the  line  joining  all  is  the  longest. 

This  is  the  graphical  representation  of  all  the  facts 
observed,  reduced  by  the  Clarke  atomic  weights,  as  repeat- 
edly explained. 

Even  if  looking  at  the  results  of  Stas  alone,  can  any  one 
call  these  atomic  weights  well  determined,  clustering  around 
some  mean  value  ? 

But  if  taken  at  their  worth,  if  overlooking  their  very 
notable  scattering  from  13.84  to  13.94,  that  is  over  a  full 
tenth  of  a  unit,  will  not  the  point  heavily  marked  N  be  the 
center  (in  such  case  of  gravity,  all  points  being  equally  well 
determined  count  equal  in  weight)  for  all  10  determinations 
of  Stas? 

The  value  for  that  point  is  13.894;  but  this  is  again 
exactly  |$  of  the  atomic  weight  of  oxygen  of  Clarke,  used 
in  these  calculations. 

Accordingly,  if  these  determinations  of  Stas  can  deter- 
mine anything  in  regard  to  the  atomic  weight  of  nitrogen, 
they  prove  that  it  is  exactly  fourteen-sixteenths  of  that  of 
oxygen. 

Hence  if  we  take  oxygen  at  16  exactly,  then  determina- 
tions of  Stas  give  N  =  14  exactly.  There  is  no  getting 
around  that. 

Of  course,  we  have  here  again  the  same  trouble  about 
the  silver. 

The  atomic  weight  of  Clarke,  deducted  from  the  totality 
of  the  determinations  of  Stas,  is  as  before  stated,  107.108; 


194  STASIAX    FOLLY   AND    FRAUD. 

and   is  somewhat  less  than  108  when  referred  to  O  :=  16, 
namely,  Ag  =  107.924. 

But  as  we  here  have  to  do  with  analytical  ratios  used  by 
Clarke  himself  for  nitrogen  only,  we  have  nothing  to  do 
with  the  silver  value  but  to  use  it  as  we  find  it  given  by 
Clarke  himself. 

And  in  that  case,  as  we  have  seen  in  detail,  the  atomic 
weight  of  nitrogen  comes  out  exactly  as  fourteen-sixteenths 
that  of  oxygen — from  the  very  determinations  of  Stas. 

Now  these  determinations  have  for  about  forty  years 
been  taken  to  contradict  this  result  most  decidedly. 

Why  has  not  some  one  of  the  Stasian  Re-Calculators 
noticed  the  fact  so  palpable  in  our  diagram  of  the  plain, 
actual  data  given  by  Stas  himself? 

This  is  one  of  the  mysteries  of  Stas  and  his  School, 
officially  recognized  throughout  the  world  of  chemistry  for 
forty  years. 

Stas  and  his  School  denounce  imagination  and  pretend 
to  give  facts,  and  exact  facts  only. 

The  fact  is  they  play  with  facts,  reduce  them  en-bloc,  a 
whole  group  of  them  at  once — so  they  can  not  tell  one  from 
the  other. 

The  method  of  reduction  used  by  Stas  is  like  the  olla 
podrida  of  the  Spanish. 

Throw  everything  from  the  dining  table  into  it,  as  it  is 
"leftover"  or  obtained  in  the  experiments;  then  take  out 
as  you  need  it,  and  don't  mind  the  odor  nor  the  error. 

In  the  same  way,  but  on  a  most  magnificent,  truly 
American  scale,  Clarke  proceeds  in  his  Smithsonian  Con- 
stants of  Nature,  and  has  produced  the  most  nauseating 
chemical  olla  podrida  that  ever  was,  and  we  hope,  ever 
will  be. 

We  have  now  twice,  holding  our  nose,  taken  out  from 
this  chemical  olla  podrida  a  full  set  of  Stasian  determina- 
tions; and  when  considering  them,  without  regard  to 
anything  else,  only  as  experimental  determinations  made 
for  the  chemical  determination  of  the  atomic  weight  of 
nitrogen,  and  proceeding  in  the  ordinary  way  of  the  art, 
using  the  auxiliary  values,  as  furnished  by  the  Stasian  Grand 


THE    MEANEST    "MEAN.'7  195 

Mogul  Clarke,  we  find  N  =  14  if  we  reduce  the  result  to  the 
standard  O  =  16. 

So  far  as  the  two  great  series  of  determinations  of  Stas 
for  the  atomic  weight  of  nitrogen  are  concerned,  they  give 
N  =.  14  exactly  for  O  =.  16. 

But  we  do  not  need  them  ourselves;  we  have  established 
the  atomic  weight  of  nitrogen  with  a  much  higher  degree 
of  precision  by  means  of  the  weighings  of  Lord  Rayleigh. 

We  do  not  want  to  use  anything  that  has  been  in  this 
Government  olla  podrida  for  five  years! 

c.    The   Meanest  -Mean"  and   its   Impossible   Probable   Error. 

The  waste  of  time  which  the  Imperialistic  Publication  of 
Clarke  of  1897,  has  caused  me,  is  relieved  by  many  remark- 
ably fine  displays  of  "Exact  Science  as  She  Is,"  in  our 
Government  Bureaus.  We  can  only  find  room  for  a  casual 
exhibition  of  such  specimens  as  cannot  be  avoided  in  our 
course  to  establish  the  truth. 

A  couple  of  specially  rich  gems  we  shall  have  to  consider 
here. 

On  page  70  of  the  Smithsonian  "  Constants  of  Nature  *' 
of  1897,  by  Frank  Wigglesworth  Clarke,  we  find  for  the 
molecular  weight  of  silver  nitrate  "three  values"  from  the 
"general  mean  "  of  as  many  analytical  ratios  stated  to  the 
third  decimal,  and  characterized  by  a  lt  probable  error"  to 
the  fourth  decimal. 

These  three  values  differ  fully  one-tenth,  or  one  unit  in 
\hzfirst  decimal. 

If  these  means  for  silver  nitrate  differ  by  fully  o.i,  this 
difference  will  necessarily  affect  with  its  full  value  the 
atomic  weight  of  nitrogen,  obtained  therefrom  by  simple 
subtraction  of  the  constant  value  for  Ag  Oa. 

But  a  range  of  o.i  on  14  is  about  three  quarters  of  one 
per  cent!  Rather  crude  results  of  pretendedly  "exact 
science  "  that  must  not  be  questioned  outside  of  the  charmed 
imperial  circle. 

We  shall  here  more  particularly  examine  the  third  of 
these  " general  means"  from  ratio  (3),  which  is  the  one  we 


196  STASIAN    FOLLY   AND    FRAUD. 

have  just  presented,  namely,  the  ratio  of  Silver  Nitrate  to 
Potassium  Chloride.  See  p.  192  and  our  diagram  Plate  III. 

The  "  general  mean,"  which  according  to  Clarke,  repre- 
sents the  data  of  obstrvation  given  by  him  on  page  65,  is 
Ag  Oa  N  =  168.731,  with  probable  error  0.0046. 

By  subtracting  the  numerical  value  of  Ag  Os,  which 
according  to  Clarke's  atomic  weights  is  154.745,  we  obtain  the 
corresponding  atomic  weight  of  nitrogen  as  the  difference. 

Simple  subtraction  gives  us 

N  =13.986 

from  the  u general  mean"  of  the  analytical  ratios  deter- 
mined by  Marignac  and  Stas,  given  on  his  page  65,  and 
represented  on  our  page  192. 

This  value,  13.986,  therefore,  is  the  value  from  the  same 
facts  deduced  by  Clarke. 

On  our  diagram,  Plate  III,  of  the  facts,  this  value  is 
exactly  located  on  the  line  of  means  at  the  point  marked  N" 
in  the  uppermost  margin  of  our  diagram;  far  above  all  the 
actual  observations,  and  very  far  above  the  actual  values  of 
Stas. 

This  is  certainly  something  remarkable.  A  "general 
mean  "  that  is  of  so  horribly  and  despicably  mean  a  charac- 
ter as  to  crawl  away  from  the  observed  facts  of  which  it  is 
the  ''general  mean,"  ought  to  be  branded  e<  unavailable  " 
for  atomic  weight  determinations,  the  same  as  Lord 
Rayleigh's  densities  of  true  nitrogen. 

Our  Chief  Chemist  il  ivho  lives  ufon  Atomic  Weights'1'1 
(see  the  statement  of  his  lieutenant,  p.  25,  of  our  False 
Atomic  Weights  of  the  Smithsonian  Institution)  never  does 
anything  by  halves,  in  "exact  science." 

So  mean  a  Mean,  lying  far  beyond  the  facts,  especially 
those  determined  by  Stas,  must  possess  a  very  despicable 
"  Probable  Error." 

So  it  does,  indeed.  We  have  above  copied  (from 
Clarke,  p.  70)  this  lt  probable  error  "  of  that  u  general  mean" 
located  at  N"  in  our  diagram;  and  tve  have  encircled  that 
meanest  of  Means  N"  by  its  given  Probable  Error. 

In  fact,  with  a  radius  exactly  equal  to  the  probable  error 
of  0.0046  calculated  by  the  Exact  Scientist  of  our  Govern- 


THE   MEANEST    "MEAN."  197 

merit  (1.  c.,  page  70),  we  have  described  a  circle  around  that 
point  N". 

As  there  are  not  quite  16  observations,  all  told,  on  our 
diagram,  we  will  take  the  number  at  this  maximum  of  16, 
because  we  are  both  liberal  to  the  Stasians,  crediting  them 
more  than  they  are  entitled  to,  and  can  easily  extract  the 
square  root  of  that  number  so  we  all  understand  it,  namely,  4. 
Hence  4  times  the  probable  error  0.0046  of  the  mean,  will 
be  the  probable  error  of  a  single  determination;  that  is 
0.0184.  Compare  pp.  11-12  and  16-17.  Let  us  take  0.02  for 
this  value. 

We  know,  that  half  oi  all  observations  should  fall  within 
this  probable  error  of  a  single  observation  (see  1.  c.,  supra). 

Hence,  if  we  draw  a  circle  with  the  radius  2  hundredths 
around  N"  (or  exactly  four  times  the  radius  of  the  circle 
actually  drawn  around  this  point),  this  circle  should  include 
one-half  of  all  the  observed  points. 

As  a  matter  of  fact,  not  one  of  the  observed  points  will 
be  included  within  that  charmed  circle. 

All  points  observed  are  from  four  to  eight  times  as  far 
from  N"  as  the  value  of  the  probable  error  of  a  single 
observation. 

The  laws  of  probability  are  most  flagrantly  belied  by  the 
results  of  Stas.  Compare:  W.  Chauvenet,  Astronomy, 
Philadelphia,  1863,  vol.  II,  p.  488. 

I  must  be  pardoned  for  the  expression  of  some  contempt 
for  the  most  rotten,  ridiculously  absurd  and  self-contradic- 
tory "Exact  Science"  of  the  Chief  Chemist  of  our 
Government,  and  for  the  expression  of  regret  that  our 
Smithsonian  has  truly  become  an  Institution  that  de  facto 
increases  and  distributes  the  worst  possible  errors  among 
men  all  over  the  globe — for  these  errors  come  in  the  garb  of 
the  highest,  most  exact  of  science,  and  are  taken  as  truth  by 
the  people — including  the  members  of  the  American  Chem- 
ical Society. 

Imperialistic  Science  can  be  depended  upon  to  rival  the 
Imperialistic  Church  of  the  past  in  producing,  diffusing  and 
upholding  error  among  men  " per  orbem." 

The  worst  crimes  laid  centuries  ago  at  the  door  of  State 


STAvSIAN    FOLLY   AND    FRAUD. 


Church  and  State  Religion  are  no  worse  than  the  rot,  rant 
and  cant  of  the  State  Science  of  to-day. 

They  cannot  call  upon  the  stake  to-day  to  annihilate  the 
independent  thinker;  but  they  know  how  to  use  the  more 
refined  and  more  cruel  methods  of  torture  available  to 
"  civilization." 


III.     CHEMICAL  ACTION  CHANGES  WEIGHT  OF  MATTER. 

But  we  are  lightly  touching  the  u  Exact  Science"  of  our 
Government  Institutions  at  Washington,  including  the 
Smithsonian  Institution  under  the  control  of  Congress. 

The  more  we  are  condemned  to  take  notice  of  the  pro- 
ductions of  the  public  printing  press  of  our  Government  in 
science,  the  more  astonished  we  become  at  the  absolute  lack 
of  understanding  of  even  the  rudiments  of  science  and  logic 
displayed  in  these  imperialistic  publications. 

There  is  not  a  chemist  "  per  orbern  "  who  believes  that 
chemical  combination  affects  the  weight  of  matter;  for  he 
knows  there  is  not  a  particle  of  evidence,  not  a  solitary 
experiment,  in  favor  of  such  an  effect. 

On  the  contrary,  it  is  held  as  an  axiom,  not  only  by  all 
chemists,  but  by  all  natural  philosophers  as  well,  that  the 
'weight  of  any  material  particle  is  entirely  independent  of  its 
state  of  chemical  combination. 

But  these  Government  "  Constants  of  Nature'''1  produced 
by  the  harmonious  interactive  co-operation  of  the  highest 
departments  and  all  at  public  expense,  do  declare,  as  a 
result  of  the  "Exact  Science"  which  has  produced  these 
"•variable  constants'*'*  that  are  " contrary  to  nature"  that 
as  a  matter  of  fact,  potassium  chloride  possesses  a  weight 
quite  different  from  the  sum  of  the  potassium  and  chlorine 
contained  therein. 

I  was  indeed  struck  with  awe  and  admiration  for  the 
Exact  Science  of  our  Government  when  first  I  noticed  this 
great  new  fact  on  page  334  of  said  (<  Constants  "  of  1897. 

I  have  since  found  that  this  great  and  marvelous  annihi- 
lation of  what  we  all  supposed  to  be  an  axiom  of  chemistry 


CLARKE'S  DISCOVERY.  199 

and  philosophy  pervades  the  entire  big  book  of  Clarke  on 
atomic  weights,  of  1897. 

The  results  published  as  the  most  probable  values  of  the 
atomic  weights,  according  to  S.  P.  Langley,  the  Secretary  of 
the  Smithsonian  Institution  (1.  c.,  p.  Ill)  are  all  dependent 
upon  this  destruction  of  the  old  axiom. 

If  the  old  axiom,  that  chemical  combination  or  decom- 
position has  no  effect  on  the  weight  of  any  particle  of  matter, 
or  of  any  atom,  is  true,  then  the  learned  secretary  of  the 
Smithsonian  Institution  has  certified  to  a  gross  systematic 
error  that  infects  one  of  the  most  pretentious  works  on  exact 
science  which  has  ever  been  issued  from  that  institution, 
which  certainly  was  not  intended  by  its  founder  Smithson, 
to  produce  or  diffuse  such  stupendous  errors. 

This  great  and  fundamental  axiom  of  all  science  up  to 
1897,  is  cooly  and  deliberately  set  aside  in  exact  weights  to 
the  third  decimal  on  page  70  of  that  publication,  in  the  fol- 
lowing form : 

Ka       rr  38.817,  probable  error,    0.0031 
Cl        =35-179,        "  "       0.0048 


Ka  Cl  =  74.025,        "  «       0.0019 

Hence )  -we  see  a  change  due  to  chemical  combination,  an 
increase  of  0.029. 

We  must  leave  out  of  consideration  such  remarkable 
facts  presented  in  these  exact  figures  as  that  the  compound 
is  known  with  much  greater  precision  than  its  constituent 
elements,  etc. 

We  must  try  to  grapple  with  the  increase  in  weight  by 
mere  chemical  combination. 

If  the  entire  increase  falls  to  the  chlorine,  it  amounts  to 
0.03  on  35.5  or  one  on  1183. 

That  is  nearly  one-tenth  of  one  per  cent! 

How  important  such  a  chemical  fact  is  in  astronomy, 
both  of  the  present  world  and  of  its  probably  nebulous  past! 

Chemical  decomposition  will  diminish  weight,  and, 
therefore,  gravitation — the  celestial  orbits  will  widen ! 

Again,  chemical  combination  taking  place  on  a  grand 


2OO  STASIAN    FOLLY   AND    FRAUD. 

scale  in  any  cosmical  system,  the  force  of  gravitation 
increasing  one-tenth  of  one  per  cent,  the  orbits  must  con- 
tract. 

But  let  us  not  be  drawn  aside  from  our  immediate  duty 
by  the  fascinating  new  prospects  which  our  Government 
establishments  of  science  open  to  our  eyes  in  cosmos, 
present  and  past.* 

We  have  here  to  deal  with  atomic  weights  only;  let  us 
return  to  this  subject,  and  determine  the  effect  of  this  new 
axiom  on  the  value  of  the  atomic  weight  of  nitrogen,  deter- 
mined by  the  chemical  means  here  under  consideration. 

All  our  calculations  made  and  of  which  the  resulting 
values  of  the  atomic  weight  of  nitrogen  were  printed  above 
on  p.  192,  and  represented  to  scale  in  diagram,  Plate  III, 
were,  we  are  sorry  to  say,  calculated  upon  the  common 
supposition  that  as  to  weight 

Ka  Cl  =  Ka  -f-  Cl. 

Or,  to  be  quite  exact,  in  numbers,  taking  as  we  did,  the 
atomic  weights  of  Clarke,  p.  70, 

Ka=z  38.817 
Cl  =35-179 

we,  in  our  ignorance  of  mind  and  blindness  of  heart  put  the 
atomic  weight  of  the  compound  equal  to  the  arithmetical 
sum,  as  Berzelius  would  have  done, 

KaCl  =  73-996 
and  did  not  add  the  value  of  weight 

0.029 

"  produced  by  chemical  combination"  which  alone  can 
produce  the  Clarkian  value  specifically  and  separately 
given,  p.  70,  as 

Ka  Cl  =  74.025. 

For  all  determinations  of  the  atomic  weight  of  nitrogen, 
by  means  of  the  analytical  ratio  of  silver  nitrate  to  potas- 
sium chloride,  in  the  manner  fully  set  forth  in  a  preceding 

*  While  reading  this  proof,  a  Sunday  paper  brings  the  illustrated 
prediction  of  the  greater  stature  of  future  man  by  Professor  McGee,  the 
official  anthropologist.  It  is  really  too  bad  that  our  sensational  papers 
get  some  of  their  most  harmful  errors  about  scientific  matters  from  our 
"official  scientists"  at  Washington. 


CLARKE'S    DISCOVERY.  2OI 

section,  we  shall  find  the  atomic  weight  of  nitrogen  0.066 
higher  for  the  higher  value  of  the  atomic  weight  of  potas- 
sium chloride  given  by  Clarke  as  due  to  the  compound  as 
such,  in  excess  of  the  simple  sum  of  the  weights  of  the 
uncombined  atoms  of  potassium  chloride. 

In  other  words,  we  humbly  confess  that  all  our  calcu- 
lated values,  and,  therefore,  all  our  dots  on  our  diagram, 
Plate  III,  for  the  atomic  weight  of  nitrogen  dependent  upon 
the  reaction  between  silver  nitrate  and  potassium  chloride, 
are  too  low  by  0.066,  if  the  elements  potassium  and  chlorine 
increase  in  weight  to  the  extent  given  by  Clarke's  value, 
i.  e.,  0.029  per  atom  of  the  compound. 

Hence,  we  found  N"  at  a  height  0.066  above  N'  the  true 
mean  of  all  determinations,  those  of  Marignac  included. 

We  ought,  therefore,  hasten  to  change  all  these  our 
results,  obtained  by  our  old-fogy  Berzelian  notion  that  the 
atomic  weight  of  a  compound  is  obtained  by  simply  taking  the 
sum  of  the  atomic  weights  of  the  constituent  atoms. 

Surely,  to  commit  such  an  error  as  0.066  on  an  atomic 
weight  of  14  is  a  very  gross  error,  as  it  amounts  to  %  of  a 
tenth,  that  is  one  fifteenth  of  a  unit,  which  is  almost  half  of 
one  per  cent  for  N  =  14. 

It  is  entirely  beyond  possibility  that,  for  example,  Lord 
Rayleigh  could  have  committed  such  an  error,  or  that  such 
an  error  can  possibly  affect  our  N  =  14  dependent  on  his 
weighings. 

For  it  amounts  almost  exactly  to  the  very  difference 
Irhich  he  noticed  between  atmospheric  and  chemical  nitro- 
gen, and  by  which  difference  he  was  led  to  his  discovery  of 
argon  and  to  the  experimental  establishment  of  the  true 
atomic  weight  of  nitrogen. 

And  I  am  especially  sorry  and  most  humbly  confess  that 
my  statement  about  Stas'  determinations  for  Silver  Nitrate 
to  Potassium  Chloride,  agreeing  with  his  determinations 
from  the  synthesis  of  silver  in  fixing  the  atomic  weight  of 
nitrogen  at  ||  of  that  of  oxygen,  was  a  hasty  error,  com- 
mitted by  my  not  noticing,  in  time,  that  the  weight  of  the 
compound  is  different  from  the  sum  of  the  weights  of  its 


202  STASIAN    FOLLY   AND    FRAUD. 

constituents,  as  demanded  by  Clarke  on  page  70  and 
throughout  his  own  variable  Constants  of  1897. 

But,  upon  serious  reflection,  I  dare  not  even  make  this 
correction  of  my  stupid  error. 

For,  how  can  I,  a  poor,  independent  investigator,  know 
without  special  revelation  from  the  Exact  Scientists  of  our 
National  Government,  how  much  this  change  in  weight 
amounts  to  in  the  synthesis  of  silver  nitrate? 

It  is  very  true,  I  have  carefully  copied  the  Clarkian 
values  for  silver  and  oxygen,  and  used  the  sum  154.745  to 
represent  Ag  Os  in  the  silver  nitrate  in  all  my  calcu- 
lations. 

May  not  this  be  also  wrong?  Although  the  Chief  Chemist 
Clarke,  has  used  that  same  value  himself — he  may  ere  this 
have  discovered  how  much  the  one  silver  and  three  oxygen 
in  silver  nitrate,  differ  in  weight  from  the  sum  of  their 
weights  in  the  free  and  uncombined  state,  and  may  it  not  be 
that  he  simply  has  not  yet  through  the  Smithsonian  Press 
and  the  Journal  of  the  American  Chemical  Society  informed 
the  expectant  chemical  world  of  the  precise  amount? 

As  I  now,  at  last,  come  to  grasp  the  full  import  of  the 
overthrow  of  our  old  axiom  of  the  constancy  of  weight  of 
matter,  irrespective  of  chemical  combination — I  think  we 
are  really  entirely  at  the  end  of  all  possible  atomic  weight 
determinations. 

If  the  sum  of  the  weights  of  the  constituents  is  no  longer, 
according  to  Clarke,  to  be  taken  as  the  weight  of  the 
compound,  all  atomic  weight  determinations  must  cease, 
because  they  become  both  absurd  and  impossible. 

Every  new  compound  we  might  draw  upon,  would  present 
us  another  unknown  change  in  weight,  and  hence  we  would 
have  a  system  of  indeterminate  equations. 

If  Clarke  is  right— as  of  course  he  must  be,  as  Imperial- 
istic Chemist  for  the  United  States  of  America,  by  position 
and  by  his  assumption  and  by  the  recognition  his  official 
station  secured  from  the  American  Chemical  Society— all 
atomic  weight  determinations  must  cease,  having  become 
impossible. 


CLARKE'S  DISCOVERY.  203 

This  is  a  very  sad  termination  for  especially  two 
reasons. 

First,  it  will  be  apparently  impossible  for  the  u  high 
authority/'  Clarke,  to  continue  "  to  live  upon  this  subject 
of  atomic  weights  "  any  longer  at  our  National  Capital;  see 
letter,  p.  25,  of  my  "  False  Atomic  Weights  of  the  Smith- 
sonian Institution." 

Second,  the  school  of  Stas  has  always  proclaimed  that 
it  was  Stas  who  demonstrated,  by  his  experiments,  the 
unchangeability  of  the  weight  of  matter. 

This  we  see  in  the  great  Stasian  Apostle  Ostivald^  under 
the  name  of  "  die  Erhaltitng  des  Stoffes"  pp.  4-5  of  his 
Physikalische  Chemie,  II  edition,  Leipzig,  1891.  On  page 
14  of  the  same  work,  Ostwald  ascends  to  the  declaration 
that  Stas  -worked  to  the  ten-millionth  exactly,  and  asserts  that 
in  no  branch  of  science  such  -wonderful  accuracy  or  exactness 
has  been  obtained  as  in  these  determinations  of  Stas. 

UO  come,  let  us  worship  and  fall  down"  before  this 
Greatest  Master  of  Modern  Science.  (Venite,  exultemus 
Domino.) 

And  now,  all  this  glory  of  Stas,  proclaimed  from  Leipzig 
University,  falls  to  the  ground  by  the  one  modest  little  line 
in  our  own  Clarke's  Variable  Constants,  not  of  Nature — that 
Potassium  Chloride  weighs  appreciably,  yea  very  consider- 
ably, more  than  the  sum  of  the  weights  of  its  constituent 
elements. 

How  sad  my  kind  and  good  friend  Ostwald  will  be  when 
he  learns  of  this  terrible  ending  of  all  fixed,  definite  pro- 
portions in  chemistry,  of  all  attempts  at  determination  of 
atomic  weights,  and  that  all  the  glorious  precision  of  even 
his  own  Great  Master  Stas,  was  nothing  but  a  mere  shadowy 
imagination.  "  Vanity  of  Vanities." 

It  is  true,  Ostwald  has  close  at  hand  this  great  work  of 
Clarke  on  the  "  Constants  of  Nature." 

Ostwald  has  indeed  "reviewed"  this  work  of  Clarke — 
but  he  has  not  done  the  work  justice,  has  not  studied  it 
properly,  for  he  does  not  mention  this,  the  most  striking 
and  astonishing  discovery  of  Clarke. 

Herr  Geheimrath  Wilhelm  Ostwald,  of  Leipzig,  should 


2O4  STASIAN    FOLLY   AND    FRAUD. 

take  that  work  of  Clarke  of  1897,  produced  by  our  National 
Government  and  its  Scientific  Institutions,  which  are  the  most 
costly  on  earth,  containing  the  most  despotic  and  fanatic 
scientific  (.<*)  men  on  the  globe,  and  study  it  again  and  again, 
and  then  study  it  more  carefully  still. 

He  would  then  find  that  his  declaration  (Zeitschrift,  Bd. 
23,  p.  187;  1897)  was  too  hasty — namely,  that  the  estimation 
of  value  or  weight  of  determinations  used  by  Clarke,  is 
nonsense  (hat  keinen  Sinn) ;  is  simply  Furor  ClarkiL 

When,  upon  such  more  careful  reading  of  the  work  of 
Clarke,  our  gentle  friend  Ostwald,  verifies  my  recognition 
here  given  of  the  annihilation  of  our  common  foolish 
notion  of  the  constancy  of  weight,  Professor  Ostwald  will 
beg  Clarke's  pardon  and  acknowledge  meekly  his  stupidity 
and  error,  as  I  have  done  above. 

And  then,  Professor  Ostwald  and  myself,  will  as  two 
penitent  brothers,  join  hands,  and  feel  happy  that  the  Great 
American  Nation  maintains  at  the  cost  of  many  millions  of 
dollars  a  year,  stupendous  scientific  Institutions,  Bureaus 
and  What-Nots,  in  which  the  most  eminent  scientists  have 
been  living  on  atomic  "weights,  until,  at  last,  these  atomic 
weights  have  given  out. 

Lavoisier  is  pointed  out  by  Kopp  (in  his  Geschichte  der 
Chemie,  II,  p.  73)  as  the  chemist  who  first  made  a  formal 
statement  of  the  indestructibility  of  matter — or  to  speak 
more  scientifically,  die  Eihaltung  des  Stojfes.  The  old 
Greeks  had  a  notion  of  that  sort,  but  that  does  not  count 
before  exact  chemists. 

This,  retained  by  chemists  till  the  present,  implies  that 
the  weight  of  a  compound  is  equal  to  the  sum  of  weights  of 
its  constituents.  Berzelius  never  doubted  this  axiom,  but 
based  all  his  work  upon  it. 

This  pretended  axiom  has  been  demonstrated  to  be  false 
by  Clarke  in  his  famous  Constants  of  Nature,  edition  1897, 
on  pages  70,  108,  324,  334  formally,  and  throughout  the 
entire  book  in  all  its  final  results. 

With  this  grand  discovery  of  the  Chief  Chemist  Clarke, 
chemistry  of  precision  suddenly  terminates  in  a  sort  of 
RAGNAROK  that  must  involve  the  Constants  of  Nature  and 


STASIAX    HERESY.  205 


the    Workshop   where   these   constants  were  manufactured, 
and  the  great  Manufacturer  of  Atomic  Weights  himself. 
Sic  transit  gloria  mundi. 

IV.     HERESY  IN  THE  CHURCH  OF  STAS. 

It  is  surely  bad  enough  for  our  great  chemist  of  the 
United  States,  the  Chief  Chemist  of  the  Department  of  the 
Interior  and  of  the  American  Chemical  Society,  to  ruth- 
lessly destroy  our  old  faith  in  "die  Erhaltung  des  Stojfes" 
which  was  transmitted  to  us  through  our  Chemical  Saint 
Lavoisier  from  the  Greek  Sages;  but  for  Frank  Wiggles- 
worth  Clarke  to  ignore  the  highest  chemical  authority  of 
Berlin  is  too  much  for  me  to  stand  without  some  action. 

In  addition  to  this  scientific  reason,  I  have  also  a  per- 
sonal reason  to  feel  the  insult  to  the  great  official  German 
Chemist;  for  it  was  the  abandonment  of  Schleswig-Holstein 
by  Prussia,  after  having  urged  us  poor  peasants  on  into  war 
against  Denmark,  that  brought  me  to  Copenhagen,  and 
later,  when  the  appetite  for  our  land  became  whetted  in 
Berlin,  made  it  necessary  for  the  German-born  to  pull  up 
stakes  and  go  to  Egypt.  Really,  I  sometimes  feel  as  if  I  had 
been  sold  by  my  German  brethren,  as  was  Joseph  of  old  by 
his  brothers. 

Der  Herr  Geheime  Regierungs-Rath,  Hans  Landolt,  first 
Professor  of  Chemistry  of  the  University  of  Berlin,  has 
demonstrated  experimentally,  that  chemical  combination 
has  no  sensible  effect  on  the  weight  of  matter.  His  experi- 
ments are  much  more  delicate  than  even  those  of  Stas;  for 
all  weighings  are  given,  in  print,  to  the  thousandth  of  a  milli- 
gramme^  while  Stas  did  never  go  below  the  tenth  and  then 
lumped  it  by  12  to  66  milligrammes,  when  necessary. 
Besides  Landolt's  individual  experiments  extend  over  a  long 
period  of  time — up  to  several  years.* 

Der  Herr  Professor  Hans  Landolt  has  presented  (vorge- 
tragen)  his  results  at  the  meetings  of  the  Royal  Prussian 
Academy  of  Sciences,  at  Berlin,  on  March  12,  1891,  and  on 
February  4,  1892.  The  entire  research  is  published  in  the 

*  Erste  Reaktion  from  October,  1890,  to  March,  1892. 


2C>6  STASIAN    FOLLY   AND    FRAUD. 

Sitzungsberichte  der  Kgl.  preuss.  Akad.  der  Wissenschaften, 
for  1893,  PP-  3O1  t°  334.  This  is  really  the  original  publica- 
tion, and  should  properly  be  given  as  the  original  source 
whenever  this  research  is  referred  to. 

It  is  disgusting  to  find  this  great  work  published  in  full 
in  the  Zeitschrift  of  Ostwald,  Leipzig,  without  any  reference 
to  the  Academy  which  has  published  it  in  its  Transactions. 
The  one  great  reason  for  the  support  of  such  academies  is 
found  in  the  publication  of  their  Transactions.  When  such 
plebeyan  editors  as  Ostwald  can  publish  such  researches  as 
original  contributions  to  their  journals,  the  very  existence  of 
the  great  academy  of  science  is  being  undermined. 

The  United  States  Patent  Office  also  robs  the  Sitzungsbe- 
richte of  the  scientific  discoveries  of  Professor  Emil  Fischer, 
assignor  to  C.  F.  Boehringer  &  Soehne ;  elaborate  formulae 
and  all. 

Not  enough  that  Editor  Ostwald  publishes  these  great 
researches,  even  in  advance  of  their  official  publication  by 
the  academies  concerned,  the  chemical  public  is  syste- 
matically kept  misinformed  about  these  original  publica- 
tions, so  that  the  "Jahrbuch"  and  in  fact  practically  all 
chemical  records,  ignore  the  academies,  and  exclusively  refer 
to  the  piratical  (?)  journals. 

Thus  the  great  research  of  Landolt  is  commonly  credited 
to  Ostwald's  Zeitschrift  (Bd.  12,  pp.  1-34;  1893);  also  to 
Berichte  d.  D.  Chem.  Ges.  1893;  26,  1820.  I  have  not  seen 
one  publication  referring  this  research  to  the  true  source, 
the  Sitzungsberichte  of  the  Academy  of  Sciences  of  Berlin. 
Of  course,  I  have  dutifully  given  the  proper  reference,  see 
True  Atomic  Weights,  1894,  p.  39,  where  the  remarkable 
opening  sentence  of  Professor  Landolt  is  quoted  in  English 
translation. 

This  same  Editor  Ostwald  has  acted  in  the  same  bad 
spirit  toward  the  Academy  of  Sciences  of  Copenhagen  by 
printing  great  researches  presented  by  Julius  Thomsen  (in 
Danish)  to  this  academy  as  original  contributions  (in 
German)  to  his  Zeitschrift  fur  Physikalische  Chemie,  and 
issuing  this  German  paper  long  before  the  Danish  original 
appears  in  the  Ovcrsigt. 


STAS  IAN    HERESY.  2OJ 


How  Editor  Ostwald  gets  such  manuscripts  out  of  the 
archives  of  these  academies  is  quite  remarkable,  and  ought 
to  be  investigated. 

Now  this  truly  wonderful  chemical  research  of  the 
highest  chemical  authority  at  Berlin — and  consequently  of 
the  world — is  absolutely  ignored  by  our  Chief  Chemist; 
the  name  Landolt  is  not  even  contained  in  the  index  to 
authorities  of  the  Constants  of  Nature  of  1897. 

And  yet  this  research  of  Landolt  deals  exclusively  with 
die  Erhaltung  des  Stoffes.  By  this  research  it  is  experi- 
mentally demonstrated  that  chemical  action  is  totally  with- 
out influence  upon  the  weight  of  matter  itself.  The  limit  of 
precision  has  been  carried  to  the  very  utmost  in  these 
researches. 

Herr  Professor  Hans  Landolt  is,  of  course,  thoroughly 
convinced  of  the  extraordinary  exactitude  of  the  work  of 
Stas — he  begins  and  ends  with  emphatic  declarations  to  that 
effect. 

Now,  here  it  is  where  ordinary  chemists  are  placed  in  a 
dilemma. 

Both  the  greatest  chemical  authority  of  Europe  and  the 
greatest  chemical  authority  of  America,  are  firm  and  pro- 
found Stasians;  and  Stas  himself  used  all  his  skill  to  produce 
" total  syntheses"  which  rest  for  their  demonstrative  force 
on  die  Erhaltung  des  Stoffes. 

Yet,  without  even  referring  to  this  great  work  of  Lan- 
dolt, Clarke  completely  ignores  that  principle  and,  with  true 
and  most  becoming  modesty,  quietly  used  his  own  grandest 
discovery  of  modern  science,  namely,  that  "  mass "  or 
"  weight  in  a  given  place  "  does  depend  upon  chemical  com- 
bination. 

Clarke  has  not  even  mentioned  this,  his  most  wonderful 
discovery,  in  -words — he  has  simply  stated  it  in  numbers, 
as  a  fact. 

Si  Quaeris.  Circumspice ! 

Like  that  great  Architect  Wren,  of  England,  he  seems 
quietly  to  wait  till  the  chemical  world  shall  look  about;  it 
will  then  recognize  his  most  astounding  discovery. 


208  STASIAN    FOLLY   AND    FRAUD. 

And  it  is  magnanimity  which  has  prevented  him  in  1897, 
from  referring  to  Landolt's  research  of  1893.  If  he  had 
mentioned  Landolt,  he  would  have  been  compelled  to  say 
that  Landolt's  "point  of  view  is  so  radically  different  from 
"  mine  that  I  have  been  unable  to  make  use  of  his  discus- 
"  sions."  Constants,  p.  6. 

Or,  perhaps,  he  would  have  regretfully  remarked,  as  he 
does  (p.  60)  about  Lord  Rayleigh's  experimental  determi- 
nations: ' '  the  research  of  Landolt  is  unavailable  for  any 
discussion  of  atomic  weights.  Perhaps,  at  some  future 
time,  the  figures  of  Landolt  may  be  so  corrected  as  to  be 
useful  in  atomic  weight  calculations." 

I  am  sorry  to  see  the  American  Stasian  Clarke  find  it 
possible  to  demonstrate,  by  the  glorious  concordance  of  all 
the  determinations  of  Stas,  that  chemical  combination 
changes  the  weight  of  matter,  while  the  German  Stasian 
glories  in  having  confirmed  the  fundamental  result  of  all 
work  of  Stas,  that  chemical  combination  has  no  effect  what- 
ever on  the  weight  of  matter. 

Indeed,  it  would  give  me  unspeakable  joy  if  these  highest 
chemical  authorities  of  Europe  and  America  and  both  high 
Government  Scientists — although  not  yet  both  de  facto 
Imperial  Scientists — could  as  faithful  disciples  of  the  one 
and  only  Exact  Chemist,  Stas,  unite  and  agree  on  what  it  is 
that  Stas  has  established  with  such  wonderful  precision. 

What  proportions  this  Schism  in  the  Church  of  Stas  will 
assume  I  dare  not  contemplate.  I  shudder. 

Both  these  greater  authorities  are  fanatic  disciples  of 
Stas;  both  declare  all  question  about  the  exact  commensura- 
bility  of  the  atomic  "weights  definitely  settled  BY  STAS,  and 
against  the  possibility  of  such  commensurability  as  N  :  O  — 
14  :  16  =  7  :  %  exactly,  or  C  :  Orri2  :  i6r=  3  :  4  exactly. 

See  the  quotation  of  the  opening  sentence  of  Landolt  in 
True  Atomic  Weights,  p.  39,  "  Bekanntlich " 

Of  course,  both  these  greatest  Apostles  of  Stas  stand 
upon  the  solid  ground  of  experiment — from  the  hundredth 
to  the  ten-thousandth  of  a  milligramme!  Both  of  these 
leading  Apostles  of  Stas  are  destitute  of  and  abhor  imagina- 
tion— of  any  general  principle  of  absolute  science  (mathe- 


CONCLUSION.  20$ 


matics)  or  old  fogy  belief  in  the  highest  truths  of  a  Pytha- 
goras or  a  Plato. 

Our  showing  up  of  their  fancied  weighings  to  the  thou- 
sandth of  a  milligramme  by  the  simple  use  of  their  pencil 
and  paper,  is  of  course  nothing  but  what  might  be  expected 
of  such  a  heretic  barbarian  who  dares  think  truth  higher 
than  authority  of  position  or  decoration. 

However,  to  see  the  Church  of  Stas  split  upon  the  old 
rock  of  die  Erhaltting  des  Stoffes — the  permanence  of  matter 
in  weight — is  enough  to  sadden  even  the  heretic,  who  now 
must  fear  they  will  let  the  fires  go  down  and  thus  not  burru, 
him  quickly  at  the  stake,  but  just  slowly  smother  and  smoke 
him. 

Here  endeth  the  Reductio  ad  Absurdum. 


C.     THE    CONCLUSION. 


Our  Standard  Atomic  Weights  have  been  Proved  to  be  the  True 
Absolute  Atomic  Weights  of  the  Chemical  Elements. 

We  shall  not  carry  this  work  any  further;  we  shall  rest 
our  case  here. 

Those  who  still  may  claim  to  be  not  fully  satisfied,  we 
shall  not  trouble  any  further  with  reasons  or  facts. 

Our  standard  atomic  weights  gave  us  the  numerical 
values  of  the  standard  atomic  weights  of  all  the  compounds 
used  in  atomic  weight  determinations. 

A  simple  division  then  gave  us  the  standard  atomic  ratio, 
which  we  calculated  to  five  decimals. 

This  atomic  ratio  was  taken  as  standard  of  comparison 
for  all  analyses  made,  each  one  of  which  was  expressed  by 
its  own  analytical  ratio,  also  calculated  to  five  decimals. 

The  comparison  of  these  analytical  ratios,  representing 
the  observed  facts,  the  chemical  analyses,  showed  through- 
out as  near  an  absolute  coincidence  with  the  calculated 
standard  atomic  ratios  as  the  degree  of  actual  precision 
attained  to  would  allow. 


210  CONCLUSION. 


Within  the  degree  of  precision  attained  in.  the  quantita- 
tive analytical  work  done  in  the  best  laboratories  by  the  best 
chemists  of  the  nineteenth  century,  the  coincidence  was 
perfect. 

That  proves  the  statement  made  in  general  terms  at  the 
head  of  this  closing  chapter. 

The  very  fact  that  practically  all  modern  analysts  have 
done  their  work  as  opponents  to  the  law  affirmed  and 
established  by  us  upon  the  very  experimental  determinations 
of  these  chemists,  gives  a  greatly  enhanced  value  to  our 
demonstration. 

Let  us  for  a  moment  turn  to  the  excellent  laboratory 
work  of  Crookes,  taken  by  himself  as  absolutely  and  per- 
manently establishing  the  absence  of  any  commensurability 
in  the  atomic  weights  of  chemical  elements. 

It  will  be  remembered  that  every  circumstance  and 
feature  of  this  laboratory  work,  when  freed  from  errors  and 
false  data  of  reduction,  proclaims  the  conclusion  placed  at 
the  head  of  this  chapter. 

The  Maxim  of  Chee  in  Lun-Gnee. 

There  is  one  accusation  of  "  selection  "  made  by  Crookes 
in  his  denunciatory  editorial  of  1896,  to  which  I  had  written 
a  lengthy  and  naturally  a  very  caustic  refutation ;  but  I  have 
withdrawn  this  very  interesting  and  entertaining  article,  and 
shall  simply  make  Crookes  feel  the  force  of  the  general 
argument,  given  as  closing  part  of  this  work,  without  refer- 
ence whatever  to  Mr.  Crookes  individually. 

If  Sir  William  Crookes  is  able  to  understand,  he  will 
understand,  as  one  of  my  readers.  If  he  is  not  able,  or 
perchance  still  unwilling  to  understand,  it  does  not  seem 
necessary  for  me  to  take  any  notice  thereof. 

I  shall,  in  this  matter,  follow  the  old  maxim  of  the 
Chinese  Sage  CHEE,  given  in  I,  8  of  Lun-Gnee: 

<(  Who  do  not  strive  to  learn,  to  them  I  do  not  unfold  my 
et  ideas;  who  open  not  their  minds,  those  I  do  not  instruct. 
"  When  I  describe  one  corner,  if  the  pupil  comprehend  not 
"  the  other  three,  I  do  not  repeat  my  instruction.'* 


OUR    DEMONSTRATION.  211 


Having  mislaid  the  original,  I  beg  the  readers  to  be 
satisfied  with  the  translation.  For  a  while  I  studied  the 
Chinese  language  seriously. 

The  only  modification  we  have  to  make  to  this  excellent 
maxim  to  fit  it  exactly  to  this  chemical  question,  is  in  regard 
to  the  precise  number  of  corners. 

Modern  chemists,  being  all  infected  by  the  tetrahedral 
bacillus  (Gen.  Chem.  86,  1-6;  1897)  will  require  six  corners 
of  the  full  form,  the  octahedron. 

We  have  only  presented  one  of  these  corners  in  the 
atomic  weights  of  the  thirteen  elements  considered. 

But  there  are  probably  six  times  that  many  elements. 

In  other  words,  we  have  only  described  one  corner,  out 
of  the  six  of  the  chemical  octahedron. 

Is  Our  Demonstration  General? 

Is  our  demonstration,  given  for  13  elements,  sufficient  to 
cover  six  times  that  number,  or  all  the  chemical  elements 
known,  and  even  all  not  yet  known? 

Let  us  examine  this  question  with  such  care  as  it  deserves. 
Those  versed  in  the  remarkable  accumulation  of  evidence 
by  compliance  with  a  most  special  condition,  imposed  upon 
each  one  of  a  number  of  individuals,  such  as  we  have 
discovered  in  the  cases  examined,  need  no  further  demon- 
stration. 

However,  it  may  even  to  these  readers  prove  interesting 
to  obtain  a  numerical  valuation  of  the  force  of  this  evidence. 

The  elements  made  use  of  so  far,  are  the  following  13, 
comprising  the  most  important  and  best  investigated  of  all : 

Lead,  Iron,  Mercury,  Sulphur,  Chlorine,  Carbon,  Cal- 
cium, Magnesium,  Platinum,  Thallium,  Boron,  Sodium, 
Nitrogen. 

The  experimental  data  used  in  our  determination  were 
furnished  by  the  following  eminent  chemists  in  the  order  of 
time: 

Berzelius,  1810-1830;  Pb.  —Turner,  1833;  Cl.  —Dumas, 
1840;  C.  — Erdmann  and  Marchand,  1844;  Hg,  S,  also  Ca. 
— Svanberg,  1844;  Fe.  — Scheerer,  1850-57 ;  Mg.  — Crookes, 


212  •  CONCLUSION. 


18735X1.    — Seubert,  1881 ;  Pt.    —Ramsay  and  Aston,  1893; 
Bo,  Na.     — Lord  Rajleigh,  1895 ;  N. 

This  list  of  names  comprises  none  but  first-class  chemical 
analysts  and  experimental  philosophers.  The  period  of  time 
actually  covered  is  85  years,  from  Berzelius,  1810,  to  Lord 
Rayleigh,  1895. 

The  Work  of  Four  Generations  of  Chemists. 

Some  of  the  biggest  fools  put  by  mysterious  powers  into 
positions  of  influence  for  bad  as  well  as  for  good  have  exhib- 
ited with  glee  the  enormous  dimensions  of  their  ears  and 
enjoyed  the  echo  of  their  bray,  saying:  "  Hinrichs  has  not 
made  any  new  experimental  determinations." 

Could  any  one  individual  do  the  work  here  required  that 
has  been  done  by  four  generations?  Compare  True  Atomic 
Weights,  1894,  pp.  201-204. 

It  is  true,  Stas  and  his  school,  have  studiously  and 
steadily  created  the  opinion  that  these  great  chemists  were 
mere  Tyros  compared  to  Stas;  but  we  have  shown  how 
false  this  opinion  is. 

The  great  work  done  by  these  Master  Chemists  has, 
however,  thus  far,  not  become  properly  useful  to  science, 
because  it  has  not  not  been  properly  reduced. 

The  present  condition  of  this  great  experimental  work  is 
worse  than  that  of  the  observations  of  Tycho  Brahe,  made  at 
Uraniborg,  at  the  time  he  was  driven  out  of  Denmark.  True 
Atomic  Weights,  p.  54. 

The  reduction  by  Kepler  made  the  observations  of  Tycho 
most  useful  to  astronomy. 

It  is  that  work  it  has  been  my  ambition  to  do  for  chem- 
istry in  regard  to  the  atomic  weight  determinations  of  the 
last  century. 

The  Probability  of  our  Conclusion. 

The  limit  of  precision  or  accuracy,  for  a  number  of  these 
determinations  is  as  high  as  o.ooi  at  least.  Such  are  the 
atomic  weights  of  Bo,  C,  Tl,  N.  For  less  than  this  number 
the  limit  attained  does  not  quite  reach  o.oi. 


IT'S     PROBABILITY. 


We  term  a  precision  "  high  "  when  the  limit  of  the  final 
possible  error  is  small. 

To  make  our  demonstration  as  strong  as  possible,  we  will 
suppose  the  degree  of  precision  to  be  o.oi  only  in  all  cases^ 
and  count  only  12  of  the  thirteen  elements  we  actually  have. 

On  another  occasion  we  may  take  the  full  value  of  all; 
here  we  desire  to  give  every  advantage  to  the  other  side. 

If  we  limit  the  precision  to  one  hundredth  only,  we  have 
50  such  on  either  side  of  the  atomic  weight  terminating  .00 
(to  the  hundredth  exactly).  Half  of  these  are  negative,  the 
others  positive;  in  all,  one  hundred  distinct  possible  values. 

Hence  for  any  one  element,  the  value  terminating  with 
.00  is  just  one  in  one  hundred  possible  ones. 

For  tivo  elements,  any  one  of  these  100  decimals  might  be 
combined  with  every  one  of  the  100  of  the  first;  hence,  the 
total  number  of  possible  combinations  of  such  decimals  is 
iooX  IO°  f°r  ^vo  elements. 

Only  one  combination  out  of  these  10  ooo  equally  possi- 
ble ones  is  the  one  in  which  both  atomic  weights  terminate 
in  .00. 

It  will  be  readily  seen,  that  for  twelve  elements ,  the 
chance  that  all  twelve  atomic  weights  terminate  .00  is  only 
one  in  100  raised  to  the  I2th  power,  that  is 

as  I  tO  I  OOOOOO  000000  OOOOOO  OOOOOO. 

In  case  we  had  counted  the  thirteenth  element  in,  this 
number  would  have  been  hundred  times  as  large,  and  con- 
tained 26  ciphers. 

For  every  element  for  which  the  precision  reaches  the 
thousandth,  we  would  have  gained  one  additional  cipher  in 
this  big  number. 

We  see  that  we  could  have  insisted  on  a  million  times  as 
targe  a  number  as  the  one  above  given. 

But  I  think  the  above  number  is  large  enough  for  our 
purpose  of  demonstration.  Let  us  try  to  express  the  result 
in  words. 

The  chance  that  all  the  twelve  chemical  elements  have  their 
atomic  weight^  expressed  to  the  hundredth  of  a  unit,  terminate 
-with  tivo  ciphers,  is  as  ONE  to  the  number 

I  OOOOOO  OOOOOO  OOOOOO  OOOOOO. 


214  CONCLUSION. 


Since  now  the  twelve  elements  specified  actually  do  so, 
notwithstanding  this  extraordinary  minute  chance,  they  do 
so  because  *it  is  a  Laiv  of  Nature. 

We  have  not  referred  specially  to  the  few  cases  (at  most 
5  of  50  fairly  known)  which  terminate  in  .50  instead  of  in 
.00,  as  do  chlorine  and  copper. 

In  this  case,  the  demonstration  remains  the  same  exactly, 
provided  to  either  side  there  is  the  same  distance  of  half  a 
unit  to  the  beginning  of  the  next;  in  other  words,  the  next 
full  number  must  be  distant  i%  full  units  either  way. 

We  may  also  express  this  condition  by  saying  that  where 
an  exact  half  atomic  weight  occurs,  we  can  only  have  one 
element  in  an  interval  of  three  units  between  the  neighbor- 
ing two. 

Such  is  actually  the  case  in  every  instance ;  in  fact 
ordinarily  the  distance  is  even  greater.  Thus  S  32  and  K  39 
are  the  nearest  elements  in  atomic  weight  on  either  side  of 
Chlorine,  35.5. 

Why  we  did  not  -  Select "  the  Elements. 

The  possibility  that  the  coincidence  established  by  us  as 
a  fact,  might  be  a  mere  accident,  is  absolutely  none. 

Now,  we  did  not  select  the  twelve  elements;  and  if  any 
one  were  to  try  it  he  would  have  i  oooooo  oooooo  coocoo 
ooocoo  against  one  to  fail.  He  would  fail — unless  it  were  a 
fact  of  nature;  a  law!' 

No  man  of  any  mathematical  sense  would  think  of  such 
a  possibility  of  (i  selection." 

To  find  a  single  needle  in  a  haystack  covering  the  entire 
United  States,  would  be  a  mere  child's  play  compared  to 
such  a  selection. 

I  really  suppose  that  even  Sir  William  Crookes,  great 
expert  as  he  is  supposed  to  be,  would  not  undertake  to  select 
or  find  a  needle  in  such  a  haystack,  which  I  beg  him  to 
believe,  would  be  several  times*  as  large  as  all  England  and 
Wales,  with  even  Scotland  and  Ireland  thrown  in. 

*  Fully  thirty  times. 


THAT    HAYSTACK.  215 


Find  a  Needle  in  thai  Haystack. 

When  dealing  with  a  number  so  vast  as  we  have  here 
obtained  expressing  the  certainty  of  our  final  conclusion,  it 
is  extremely  difficult  to  convey  any  sort  of  an  adequate  idea 
of  the  real  force  of  the  argument  because  the  number  itself 
lies  beyond  the  conception  of  the  human  mind. 

We  shall,  therefore,  interrupt  our  argument  for  one 
moment  longer,  in  order  to  develop  this  illustration  of 
"finding  a  needle  in  a  haystack"  in  the  manner  already 
indicated. 

Indeed,  this  conception  of  the  practical  impossibility  of 
finding  a  single  needle  lost  in  hay  stacked  up,  is  the  most 
common  and  striking  mental  picture  in  our  language 
expressive  of  a  chance  that  is  practically  zero. 

Let  us  consider  an  ordinary  rectangular  haystack  having 
a  base  a  rod  square.  Then  an  acre  will  hold  160  such  stacks, 
and  since  a  square  mile  is  640  acres,  it  will  hold  102  400  such 
stacks.  Let  us  say  100  ooo  stacks  to  the  square  mile. 

The  United  States  (including  Alaska)  are  3.6  million 
square  miles,  and  would,  therefore,  hold  360  ooo  millions  of 
such  haystacks. 

To  find  a  needle  in  the  haystack  covering  the  entire 
surface  of  the  United  States  and  Alaska,  would,  therefore, 
be  to  the  finding  of  a  needle  in  a  common  haystack  of  a 
square  rod  base  as 

i    to   360000  oooooo. 

We  see  that  this  number  is  a  mere  handful  when  com- 
pared to  our  own  number  above  given. 

If  we  extend  the  haystack  to  cover  all  America,  both 
North  and  South,  its  base  will  be  16.3  million  square  miles, 
sufficient  to  hold 

i  630000  oooooo 

such  haystacks  of  one  rod  square. 

Also  this  number  is  insignificant  when  compared  to  the 
one  expressing  the  possibility  of  the  "  selection  "  insinuated 
against  us  by  a  "high  chemical  authority"  who  likes  to  rush 
into  editorial  print  to  show  his  utter  ignorance  of  what  he 
is  talking  about  and  "  denouncing.*' 


2l6  CONCLUSION. 


Let  us  extend  our  haystack  to  the  whole  land  surface  of 
the  globe,  which  is  estimated  at  52.5  million  square  miles, 
and  it  will  hold  only  5  250000  oooooo  such  stacks,. 

To  find  a  needle  in  a  haystack  covering  all  the  land  of 
the  terrestrial  globe,  therefore,  is  a  mere  child's  play  in 
comparison  to  finding  the  one  chance  in  our  number  given 
above. 

The  entire  surface  of  the  earth,  land  and  sea,  all  counted 
in,  amounts  to  only  200  million  square  miles.  A  needle  in 
a  haystack  covering  the  entire  surface  of  the  earth  will, 
therefore,  be 

as   i   to   20  ooo  ooo  ooo  ooo, 
which  chance  is 

50  ooo  ooo  ooo 

times  greater  than  the  one  under  consideration  above. 

Now  then,  if  to  find  a  single  needle  in  a  haystack  of  a 
square  rod  base  and  say  about  a  rod  high,  is  a  chance  of  say 

i    in   50  coo, 

then  the  "  selection  "  of  12  elements  to  be  successful  in  the 
sense  above  given  is 

one  million  times 

more  difficult  than  finding  a  single  needle  in  a  haystack 
covering  the  entire  surface  of  the  earth,  both  land  and  sea. 

In  other  words,  our  haystack  must  be  a  million  times  as 
large  as  the  entire  surface  of  the  earth. 

Taking  all  the  planets  of  our  solar  system,  we  obtain  only 
a  total  surface  of  about  160  times  that  of  our  earth.  Even 
the  sun  has  only  a  surface  of  11,700  times  that  of  the 
earth. 

The  combined  surfaces  of  sun  and  all  planets,  therefore, 
is  less  than  12,000  times  the  surface  of  the  earth. 

The  haystack  covering  the  surface  of  all  bodies  of  our 
solar  system,  gives  us  less  than  the  eightieth  part  of  the  area 
required  for  the  haystack  to  contain  the  single  needle  which 
to  find  will  be  equal  to  the  chance  of  our  twelve  elements 
having  atomic  weights  terminating  in  .00  exactly. 

For  this,  our  haystack,  we  need  a  globe  having  exactly 
one  thousand  times  the  linear  dimensions  of  our  earth.  A 
town  lot  of  50  by  100  feet  on  our  earth  would  represent  a 


ATOMIC    NUMBER.  21' 


surface  about  equal  to  two  congressional  townships  on  this 
new  globe. 

A  river  valley  three  miles  wide  on  our  earth,  would  be 
like  the  Atlantic,  3,000  miles  wide. 

A  little  town  of  one  thousand  inhabitants  on  our  earth 
would  be  represented  by  1,000  millions  of  inhabitants. 

The  entire  sun  would  be  only  one-tenth  in  dimension, 
one-hundredth  in  surface,  of  this  required  globe. 

To  find  a  single  needle  in  a  haystack  covering  this  globe, 
the  surface  of  which  is  a  million  times  that  of  our  earth,  is 
exactly  the  same  chance  as  that  the  atomic  weights  of  twelve 
elements  are  full  numbers  to  the  hundredth  of  a  unit  exactly, 
by  chance. 

Now,  as  these  twelve  elements  actually  do  so  terminate 
in  fact,  this  fact  is  not  a  matter  of  chance,  but  due  to  a  Law 
of  Nature. 

This  is  the  best  I  can  do  to  give  the  reader  any  concep- 
tion of  the  meaning  of  the  chance  expressed  in  the  number 
above  given,  that  unit  followed  by  twenty-four  ciphers. 

Why  our  Demonstration  Applies  to  All  Elements. 

But  since  we  have  not  selected  the  dozen  elements,  except 
for  the  fact  that  the  analytical  work  done  was  the  most 
perfect  (such  as  done  by  Berzelius  and  Crookes,  by  Ramsay 
and  Lord  Rayleigh),  then  this  calculation  applies  to  any 
twelve  out  of  the  total  number  of  elements. 

Accordingly ',  this  calculation  does  apply  to  all  the  chemical 
elements  ! 

The  mathematical  expression  of  this  great  natural  fact, 
may  be  stated  in  the  following  words: 

The  atomic  weights  of  all  chemical  elements  are  exactly 
commensurable  ; 

The  greatest  common  diznsor  of  all  is  the  twenty-fourth 
part  of  the  atomic  -weight  of  diamond-carbon. 

The  Atomic  Number. 

If  then,  we  take  this  weight  as  unit  and  call  it  the  atomic 
iveight  of  pantogen,  the  atomic  weight  of  all  chemical 


2l8  CONCLUSION. 


elements  will  be  some  definite  natural  number,  expressing 
the  number  of  pantogen-atoms  having  the  same  weight  as 
the  atom  of  that  element  concerned. 

These  numbers  we  might  call  atomic  numbers ;  or  in 
German,  atomzahlen. 

From  what  was  incidentally  stated  in  regard  to  the 
termination  .50,  it  follows: 

The  even  atomic  numbers  are  at  least  ten  times 
as  numerous  as  the  odd  atomic  numbers. 

The  fact  is  all  we  care  for  here;  the  meaning  shall  be 
developed  on  some  other  occasion. 

The  Honorable  Secretary  of  Berlin. 

Such  a  table  of  atomzahlen  I  sent,  almost  fifty  years  ago, 
to  the  Hon.  Secretary  of  the  Physical  Society  of  Berlin, 
Professor  A.  Kronig.  See  Programme  der  Atomechanik, 
Iowa  City,  1867;  p.  3;  also  True  Atomic  Weights,  1894;  p.  3. 

In  1863  this  same  German  Professor  published  this  system 
as  his  own*  in  a  text  book  on  chemistry  and  also  pp.  53-60, 
in  his  "  Neues  Verfahren  "  against  Liebig. 

Such  a  table  of  atomic  numbers,  we  obtain  by  simply 
doubling  our  standard  atomic  weights. 

This  evidently  implies  the  Unity  Matter  or  the  composite 
nature  of  the  chemical  elements,  and  their  resulting  from 
the  condensation  of  one  single  primitive  substance,  which 
we  have  called  PANTOGEN. 

Thus,  an  atom  of  hydrogen  consists  of  2  pantogen  atoms; 
C  of  24,  O  of  32,  Hg  of  400,  Pb  of  414,  Fe  of  112,  S  of  64. 

We  shall  not  enter  upon  this  subject  at  this  place.  See 
Part  III  of  our  True  Atomic  Weights,  pp.  205-256;  1894. 

*  If  the  brutal  editorial  of  Crookes,  in  his  Chemical  News  of  May  15, 
1896,  has  any  meaning  at  all,  it  endorses  this  "new  proceeding"  on  the 
part  of  the  Secretary  of  the  Physical  Society  of  Berlin;  but  most  people 
will  call  this  act  of  Dr.  A.  Kronig  a  most  infamous  kind  of  a  steal. 

For  some  years,  I  actually  supposed  that  only  among  German 
Scientists  such  moral  scoundrels  could  be  found. 

I  have  since  learned,  by  experience,  that  I  was  mistaken  in  this 
opinion. 


PART  FOURTH. 

Tabular  View  of  the 

ATOMIC  WEIGHT  ANALYSES 

Of  the  Nineteenth  Century. 

INTRODUCTION. 


It  was  our  intention  to  give  a  complete  summary  of  all 
determinations  made  during  the  nineteenth  century.  See 
page  85. 

But  this  work  has  assumed  considerably  larger  dimen- 
sions than  anticipated. 

It  is  also  of  the  utmost  importance  to  limit  it  in  size  so 
as  to  make  it  possible  to  secure  a  wide  circulation  demanded 
by  the  subject  and  the  object. 

We  have,  therefore,  culled  our  complete  set  of  cards  and 
omitted  all  really  worthless  determinations,  as  well  as  repe- 
titions. 

Thus,  the  work  on  lead,  Part  Second,  is  simply  referred 
to,  but  not  tabulated  again. 

Also,  student's  work  on  hydrogen  generation  by  zinc, 
it  has  not  been  deemed  necessary  to  give,  as  it  was  scientif- 
ically worthless  (see  under  Zn). 

In  one  place  the  chemical  work  was  so  inspiring,  that  we 
improved  upon  Heine  and  left  out  many  worthless  figures. 

The  order  of  arrangement  is  alphabetical,  after  the 
chemical  symbol  of  the  element,  which  order  we  find  most 
convenient  for  chemists. 


220  ATOMIC    WEIGHT   ANALYSES. 

A  few  elements  have  found  no  record  at  all ;  no  serious 
work  of  permanent  value  could  be  found. 

The  non-valent  elements  have  been  omitted,  for  the 
present  time.  Theoretically  they  are  most  important;  see 
General  Chemistry,  1897,  pp.  380-381,  and  Principles,  1874, 
pp.  180-181. 

These  non-valent  elements  will  be  fully  considered  in  a 
contemplated  special  work  on  the  unity  of  matter. 

In  several  places  we  have  made  use  of  a  contracted  form 
of  tabular  representation,  as  already  done,  page  100. 

We  found  it  sufficient  to  give,  first,  our  absolute  atomic 
ratio ;  second,  the  chemical  formula  of  the  substance  and 
product  actually  used;  third,  the  extremes  and  range,  and 
fourth,  the  analytical  excess  of  the  mean, 

It  will  readily  be  seen  that  these  four  particulars  really 
are  fully  sufficient  and  imply  all  the  details  essential. 

To  a  few  elements  we  have  devoted  more  space  than  may 
seem  proper;  for  example,  to  arsenic.  But  on  careful  read- 
ing, it  will  be  found  that  nothing  could  have  been  omitted 
without  real  loss  to  the  subject. 

This  record  furnishes  an  excellent  indication  of  analyt- 
ical work  urgently  needed. 

But  in  order  to  be  available,  the  fields  thus  indicated 
must  be  worked  thoroughly  and  conscientiously. 

We  must  cease  to  run  hobbies,  to  follow  routine;  we 
must  again  be  severe  in  the  choice  of  methods,  as  in  the  first 
half  of  the  nineteenth  century. 

The  methods  of  the  school  of  Berzelius  must  be  revived, 
and  checked  by  our  methods  of  calculation  and  criticism. 

At  the  same  time  the  severity  of  our  requirements  are 
revealed  in  our  finding  it  impossible  to  assign  a  definite 
atomic  weight  for  several  elements  for  which  numerous 
determinations  have  been  made,  all  more  or  less  con- 
flicting. 

Thus,  for  palladium  the  value  106  has  generally  been 
accepted,  and  106.5  seems  to  result  from  Reiser's  determi- 
nations. But  these  results  are  probably  all  too  high. 


221 


Upon  most  carefully  revising  the  determinations  at  hand, 
for  the  completion  of  this  fourth  part,  I  had  to  drop  several 
elements  for  which  the  standard  atomic  weights  seemed 
reasonably  well  determined,  such  as  Pd,  Sr. 

We  need  thoroughly  independent  analytical  work  for 
such  elements.  Keiser  is  too  much  given  to  "  confirm " 
what  is  current,  and  Richards  is  too  much  in  the  wet  way,  to 
attach  real  value  to  their  determinations  for  these  metals. 

Ag=108.  SILVER.  MAUMENE,  1846. 

The  true  atomic  weight  of  silver  was  determined  more 
than  half  a  century  ago,  by  E.  Matiment ;  his  admirable 
determinations  were  published  in  the  Annales  de  Chimie  et 
de  Physique,  T.  18,  pp.  57-61 ;  1846.  See  also  Sebelien,  pp. 
81-82,  and  especially  my  True  Atomic  Weights,  1894,  pp. 
195-199. 

The  silver  acetate  he  prepared  in  "very  beautiful  crys- 
tals" (Nos.  1,2);  of  which  a  large  lot  he  recry stall ized  with 
extreme  care  for  determinations,  Nos.  3,  4,  the  purest  he 
was  able  to  obtain.  No.  5  was  made  on  a  small  scale  from 
silver  chloride. 

The  process  used  in  the  determination  is  analytically  and 
atomically  the  sharpest  we  know;  namely,  by  combustion, 
the  carbon  is  determined  as  carbon  dioxide,  as  in  the  noted 
combustion  of  the  diamond  by  Dumas,  while  metallic  silver 
remains  as  residue;  in  this  case  without  loss  by  volatiliza- 
tion, the  combustion  being  effected  at  a  comparatively  low 
temperature. 

The  presence  of  a  trace  of  occluded  water  in  these  crys- 
tals will  have  no  influence  on  the  result,  as  is  perfectly 
evident.  This  was  one  of  the  determining  reasons  for 
selecting  this  process  of  analysis. 

It  is  passing  strange  that  this  in  every  manner  excellent 
work  has  been  almost  ignored  for  half  a  century;  in  Clarke's 
Constants,  the  weighings  are  given,  but  the  spirit  is  omitted, 
hence  the  record  is  a  barefaced  misrepresentation  of  the 
real  facts,  as  we  shall  see. 


SILVER. 


Silver  Acetate,  Ag.  C2  Hz  Oz  —  167. 

2  C  Oa  -,  Ag=8S  :  108^0.81  482.     Change  76  low. 
Subst.      No.          C  Oa  Ag.      Analyt.  Ratio.       Excess. 


B. 

i 

6.585 

8.083 

o.Si  467 

15  low. 

" 

2 

9-J35 

11.215 

453 

29  low. 

Purest 

Acetate  : 

A. 

3 

11  -693  5 

H-35  * 

482 

o 

" 

4 

7-358 

9.030 

484 

2  high 

Other 

Acetate  : 

C. 

5 

J6-475 

20.227 

451 

31  low. 

Mean,  Subst.  A.;  o.Si  583  i  high, 

which  corresponds  to  Ag  =  107.9987. 

Silver  Oxalate,  Aga.  Cz  04  =  196.     Same  process;  burned 
quietly  when  mixed  with  pure  sand. 


C  O2  :  Ag 

=  44  :  108 

=^0.40 

741.     Change  38 

low. 

No. 

CO2 

Ag 

Analyt.  Ratio. 

Excess. 

i 

5.835 

14.269 

0.40  807 

66  high. 

2 

7.217 

J7-754 

650 

91  low. 

3 

4-703 

11-550 

919 

22    low. 

Purer  Oxalate  : 

4 

4-387 

10.771 

730 

ii  low. 

5 

3-533 

8.674 

731 

10  low. 

Purest  Oxalate 

6 

4.658 

n-535 

5             734 

7  low. 

Clarke  gives  these  six  determinations  under  one  heading, 
without  discrimiation;  but  a  glance  at  the  result  would  show 
any  one  that  the  first  three  are  entirely  different  from  the 
last  three.  Not  having  considered  these  oxalate  determina- 
tions of  equal  importance  with  the  acetate  determinations, 
studied  by  me  in  the  original  publication  for  my  paper, 
printed  pp.  195-198  of  my  True  Atomic  Weights,  I  cannot 
now  refer  to  the  original. 

But  Sebelien  gives  all  the  data  we  need,  pp.  81-82.  He 
says  in  three  determinations  Maumene  noticed  some  red 
fumes,  the  oxalate  having  been  obtained  by  precipitating  the 
nitrate  by  oxalic  acid;  hence  these  first  three  are  not  even 
considered  by  Sebelien. 


MAUMENE.  223 


Maumene*,  thereafter,  precipitated  by  ammonium  oxalate, 
and  put  a  layer  of  metallic  copper  after  the  charge.  This 
gave  him  2  determinations  (our  Nos.  4,  5),  which,  however, 
still  showed  a  faint  trace  of  the  red  fumes.  Hence  he  started 
with  acetate,  which  after  most  careful  purification  was 
precipitated  by  oxalic  acid,  giving  him  the  purest  oxalate 
for  our  No.  6. 

Sebelien,  as  stated,  does  not  give  Nos.  i,  2,  3  at  all;  his 
No.  i  is  our  No.  4,  and  his  No.  3  is  our  No.  6. 

We  shall  take  all  determinations,  for  they  are  all  equally 
histructir'e  if  we  have  regard  to  the  established  degree  of 
purity  of  the  substance. 

Nos.  1-3,  contaminated  by  a  trace  of  nitrate,  give  greatest 
analytical  excesses,  both  high  and  low,  averaging  16  low. 
These  determinations  were  considered  by  Maumene  as 
merely  preparatory. 

He  detected  the  error,  and  eliminated  it,  oy  the  improved 
mode  of  preparation  stated. 

The  results  (Nos.  4,  5)  are  good ;  but  he  prepared  a 
sample  still  more  pure  and  got  (in  No.  6)  the  best  that  this 
method  of  analysis  can  produce. 

We  see  here  (as  well  as  under  the  acetate)  how  dread- 
fully misleading  are  even  the  statements  of  fact  in  this 
Smithsonian  Publication  of  Clarke.  His  ratios  are  also 
given  to  4  places  only. 

Indeed,  even  as  a  record  of  experimental  data,  supposed 
to  have  been  intelligently  copied,  we  are  forced  to  discard 
this  work;  manifestly  not  even  that  much  intelligence  was 
expended  upon  its  preparation,  to  furnish  a  true  copy  of  the 
actual  results,  which  of  necessity,  implies  the  statement  of 
the  greatly  varying  degree  of  purity. 

The  record,  as  here  given  by  us,  exhibits  in  the  analyt- 
ical excess,  a  most  striking  demonstration  of  the  gradual 
approach  to  the  truth  as  purity  of  substance  is  secured,  and 
gives  also  an  excellent  testimony  of  the  intelligence  of 
Maumene1  in  skillfully  approaching  perfect  purity. 

The  record,  as  given  by  Clarke,  would  condemn 
Maumene'  as  analyst.  We  do  not  say  that  Clarke  intended 


224  SILVER. 


to  create  that  impression  ;  really,  he  probably  did  not  under- 
stand the  subject  at  all. 

Now,  for  7  low  with  the  purest  oxalate,  what  would  be  the 
corresponding  atomic  weight  of  silver?  Since  7  is  less  than 
£  of  38  low  (for  o.i  high),  the  atomic  weight  of  silver  cor- 
responding to  this  analysis  is  less  than  0.02  high,  or  A&  is 
Jess  than  108.02. 

The  oxalate  process  is  necessarily  inferior  to  the  acetate 
process,  which  in  1894  I  used  alone ;  but  the  oxalate  process 
is  a  good  approximation  and  thus  offers  a  valuable  and 
instructive  confirmation. 

But  even  the  oxalate  process  of  Maumene*  is  much 
superior  in  accuracy  and  chemical  reliability  to  the  C(  famous 
determinations"  of  Stas,  which  superseded  all  good  chem- 
ical work,  but  will  now  soon  be  remembered  only  as 
infamous  impositions. 

There  can  remain  no  possible  doubt  about  the  atomic 
weight  of  silver;  it  is  found  within  o.ooi  to  be  108.  It  is  108 
exactly. 

Other  Determinations. 

Organic  Silver  Salts  weighed,  and  silver  obtained  by 
reduction,  weighed.  Loss  of  silver  almost  unavoidable. 

Liebig  and  Redtenbacher,  1840,  made  5  determinations 
each  on  the  acetate,  tartrate,  racemate  and  malate;  results 
reasonably  concordant,  but  all  means  60  to  67  low  (red.  to 
vacuum),  representing  the  atomic  weight  2  to  3  tenths  low 
(107.7). 

Maumene,  1846,  did  considerably  better  work  on  the 
acetate;  a  third  recrystallization  gave  him  only  5  low, 
corresponding  to  107.975. 

It  was  upon  the  material  furnished  by  Liebig  and 
Redtenbacher  that  A.  Strecker,  in  1846  (Liebig's  Annalen 
LIX),  for  the  first  time  inflicted  a  purely  mathematical 
curse  upon  chemistry,  by  supposing  no  errors  but  absolutely 
uniform  and  constant  ones  (how  utterly  absurd  in  chemistry) 
and  then  applied  the  formulary  of  elimination  and  the 
"  Method  of  the  least  Squares.'1'1 

The  process  and  publication  was  most  learned,  the  results 
palpably  false.  See  a  summary,  Sebelien,  73-75. 


ALUMINUM. 


Clarke  applied  this  same  process  to  cadmium  sulphate. 

Essentially  the  same  process  is  underlying  the  work  of 
Stas;  the  method  of  the  least  squares,  was  most  fully 
applied  by  our  own  Clarke,  though  Ostwald  and  Van  der 
Plaats  went  quite  far  enough  into  that  labyrinth  of  error. 

But  when  chemists  are  fool  enough  to  take  the  Mean 
as  very  nearly  the  true  value,  and  the  "  probable  error  of  the 
mean"  as  about  the  distance  from  that  mean  to  the  true 
value — we  can  expect  anything  absurd. 

Hardin,  1896,  has  subjected  small  amounts  of  acetates 
and  benzoates  to  electrolysis.  His  mean  for  the  first  is  34 
low,  corresponding  to  1.6  tenths  low  or  107.84.  This  cor- 
responds exactly  to  Stas,  for  the  true  N=ri4.  Possibly 
selection  of  results  was  made,  using  Stas  as  standard; 
Hardin  has  admitted  practicing  selection  (see  p.  100)  and 
fears  the  oracle  at  Washington. 

Silver  Nitrate,  Chloride,  and  the  entire  Mixtum  Compos- 
itum  of  StaS)  1860-1882,  wet  and  dry,  must  be  definitely 
placed  in  die  Chemische  Rumpelkammer,  as  we  have  shown 
with  sufficient  detail  in  this  work  and  in  our  True  Atomic 
Weights,  namely,  pp.  70-138. 

Methods  that  have  been  demonstrated  to  be  fallacious, 
must  be  set  aside— and  thrown  out  from  Chemical  Science 
forever. 

Al  =  27.  ALUMINUM. 

Ammonium  Alum,  Am2  Al2  (O*  8)4  -j-  24  Hz  0=906. 
Mallet,  1880,  used  two  finely  crystallized  samples  A  and  B, 
of  which  he  deems  A  the  best  chemically.  Ignition  leaves 
Ah  Oa  =  102. 

Hence,  atomic  ratio  o.  n  258,  with  20  high  for  27.1. 

Mean  of  five  determinations  lot  A  was  14  high  with  a 
range  of  12,  all  high  (from  8  to  20). 

The  mean  would  correspond  to  27.07. 

Aluminum  SulpJiate,  Ala  (O4  S)a  2^:342.  Ignition  leaves 
the  oxide,  hence  atomic  ratio  0.29  825.  Change  41  high. 

Baubigny,  1883,  made  two  determinations  giving  16  high 
and  2  low;  mean  7  high,  corresponds  to  27.017  or  say  27.02. 


226  ARSENIC. 


This  is  absolutely  nearer,  than  Mallet's  result,  and  on 
both  sides  of  the  true  atomic  value.  By  the  way,  Berzelius 
found  27.2  by  this  method. 

But  the  chemical  condition  of  the  sulphate  is  rather 
improper — not  crystalized. 

While  there  is  no  doubt  but  27  is  the  true  atomic  weight, 
new  determinations  are  urgently  called  for,  provided  good 
methods  are  used. 

Other  Determinations  have  been  made  in  considerable 
number.  The  most  pretentious  are  those  by  Mallet,  Phil. 
Transact,  1880,  p.  1003. 

Most  of  these  determinations  of  Mallet  are  made  accord- 
ing to  Stasian  methods,  hence  useless;  the  only  exception  is 
the  case  above  used,  but  that  was  very  much  neglected  bj 
him.  The  use  of  hydrogen  is  out  of  the  question,  since 
other  Stasians  have  thoroughly  discredited  it. 

Dumas,  in  1858,  used  the  chloride,  and  Mallet,  in  1880, 
the  bromide;  both  determined  by  silver. 

Such  methods  are  useless  for  a  metal  like  aluminum. 
They  sin  too  greatly  against  the  first  part  of  the  old  rule  of 
Berzelius;  for  they  depend  mainly  on  the  "skill"  of  the 
chemist,  not  on  the  fixed  conditions  of  the  substance  or  the 
process,  not  on  nature.  See  p.  3. 

Chemical  acrobats  are  no  longer  in  demand.  True  At. 
Weights,  p.  135. 

As  =  75.  ARSENIC.  EDGAR  F.  SMITH. 

The  most  reliable  work  on  the  atomic  weight  of  arsenic 
has  been  done  at  the  suggestion  and  under  the  direction  of 
Professor  Edgar  F.  Smith  in  the  John  Harrison  Laboratory 
of  the  University  of  Pensylvania. 

The  work  itself  has  been  executed  by  J.  G.  Hibbs  in  that 
laboratory;  but  we  all  know  that  the  method  and  direction 
is  the  main  thing. 

Pyroarsenate  moderately  heated  in  a  current  of  dry  muri- 
atic acid  gas  leaves   a  residue   of   salt.     Hence   the  atomic 
ratio  is 
4  Na  Cl  :  Na4  Ov  As2  =  234  :  354  =  0.66  102.    Change  38  low. 


EDGAR    F.    SMITH.  22/ 


I  have  made  a  number  of  calculations  to  obtain  cer- 
tain checks  deemed  vecy  necessary  before  placing  this  name 
at  the  head  of  so  important  an  element.  I  think  I  can  be 
reasonably  satisfied.  The  analytical  ratios  here  given  have 
been  calculated  by  myself. 

Hibbs'  Direct  Weighings  in  Milligrammes. 

No.  Salt. 

1  H-39 

2  31.14 

3  38.28 

4  269.70 

5  333-28 


Pyroarsenate. 

Analyt.  Ratio. 

Excess. 

21.76 

0.66  131 

29  high. 

47.11 

IOI 

i  low. 

57-92 

091 

it  low. 

407.80 

135 

33  high. 

504.40 

075 

27  low. 

774-97 

096 

6  low. 

828.53 

096 

6  low. 

1190.68 

088 

14  low. 

1674.64 

092 

10  low. 

3224.85 

IO2 

o  low. 

6  512.22 

7  547-62 
786.90 

9  1106.81 

10  2131.68 

Not  reduced  to  vacuum. 

Below  half  a  gramme  of  pyroarsenate  the  results  are 
necessarily  of  a  low  apparent  precision  individually;  but 
collectively,  they  give  the  mean  0.66  105  which  is  only  3 
high.  This  corresponds  to  considerably  less  than  one-tenth 
of  the  fall  for  an  increase  of  o.i  in  the  atomic  weight  of 
arsenic. 

Accordingly,  these  five  determinations,  in  which  only 
from  20  to  500  milligrammes  of  pyroarsenate  were  used,  give 
a  mean  value  75.01  for  As,  the  individual  determinations 
falling  almost  equally  to  both  sides  of  this  mean. 

The  next/b«r  determinations  Nos.  6-9,  show  a  systematic 
error,  with  a  minimum  at  No.  8.  The  mean  of  these  four 
values  is  093,  or  9  low.  This  corresponds  to  one-fourth  of 
the  tenth,  or  to  0.025  high,  that  is  As  =  75.025.  The  amount 
of  pyroarsenate  used  is  from  )•£  to  \  grammes,  averaging  a 
little  over  one  gramme. 

Finally,  we  have  the  last  determination,  No.  10,  in  which 
over  3  grammes  of  pyroarsenate  were  used.  The  analytical 
ratio  is  exactly  equal  to  our  atomic  ratio;  hence  As  =  75, 
exactly. 


228  ARSENIC. 


Suppose  we  stop  right  here,  and  ask,  what  is  the  atomic 
weight  of  arsenic  resulting  from  this  series  of  10  determina- 
tions, in  the  three  groups :  Nos.  1-5,  6-9,  10. 

Is  it  not  plain  as  day-light,  that  this  atomic  weight  is  75 
exactly,  to  which  all  determinations  approach  as  near  as 
possible  ? 

Could  anything  more  be  demanded  than  such  a  close 
approximation  ?  Does  not  such  a  gradually  increasing  series 
give  a  fine  chance  for  the  study  of  the  work,  even  though  we 
cannot  always  expect  a  perfect  trajectory  of  errors  (see  True 
At.  Weights,  1894,  p.  160). 

I  look  upon  this  experimental  work  due  to  friend  Edgar 
F.  Smith  as  the  best  work  in  atomic  weight  determinations 
produced  in  America.  See  my  General  Chemistry,  1897, 
page  378. 

Lost  in  the  Widerness  of  Error. 

Of  course,  m'y  friend  Edgar,  has,  like  many  others,  bowed 
to  authority,  to  the  great  Chief  Chemist  at  Washington,  and 
the  real  Chief  Center  of  the  American  Chemical  Society. 
Having  bowed  down  and  competed  for  minute  u  probable 
errors"  with  the  consequent  "high  weight"  in  the  hands 
of  the  Chief  Chemist,  and  a  place  in  the  Smithsonian 
Constants,  he  has  forsaken  the  God  of  Truth  and  committed 
abominations.  Clarke,  p.  263. 

Under  these  circumstances,  Edgar  F.  Smith  was  com- 
pelled to  use  the  atomic  weights  of  the  Chief  Chemist,  and 
thus  he  falsified  his  own  good  chemical  'work  by  the  use  of  the 
false  auxiliary  values  of  Clarke. 

"  Ye  cannot  serve  both  God  and  Mammon,"  it  was  said 
in  that  old  book  which  remains  true  to-day  in  human  life 
and  even  in  science. 

Therefore,  the  atomic  weight  of  arsenic  is  not  74.9158 
with  a  probable  error  of  0.00222,  as  J.  G.  Hibbs  in  his 
thesis  (p.  22)  of  1896,  reports  to  his  Professor,  Edgar  F. 
Smith. 

This  value  is  false,  resulting  from  the  reduction  of  good 
laboratory  work  by  the  false  atomic  weights  of  the  Smith- 


EDGAR    F.    SMITH.  229 


sonian  Institution,  made  by  Clarke  and  blindly  "  adopted  " 
by  the  American  Chemical  Society. 

I  have  taken  up  the  laboratory  work  done  under  the 
direction  of  Edgar  F.  Smith,  and  as  I  do  not  accept  human 
or  official  authority,  but  exclusir'cly  depend  on  Nature,  I  have 
thrown  out  the  errors  introduced  by  the  servile  use  of  the 
"official"  atomic  weights  of  Clarke  and  the  Smithsonian 
Institution. 

As  a  result  I  find  the  atomic  weight  of  arsenic  to  be  75 
exactly,  based  upon  the  actual  determinations  made. 

Thus,  Professor  Edgar  F.  Smith,  is  compelled  to  testify,  by 
his  work,  against  the  official  fraud  and  against  the  American 
Chemical  Society,  of  which  he  has  been  President. 

I  consider  this  case  a  most  important  and  highly  instruc- 
tive one. 

If  the  teachings  of  this  case  are  lost  upon  American 
chemists  who  desire  to  do  atomic  weight  work,  the  contam- 
ination by  the  rotten  science  of  Washington,  has  penetrated 
deeper  than  I  would  suppose  possible. 

No  Reduction  to  Vacuum. 

For  my  work  I  have  taken,  as  stated,  the  direct  results  of 
the  actual  weighing,  without  the  so-called  reduction  to 
vacuum.  I  really  did  not  wish  to  enter  upon  explanations, 
because  I  desired  to  avoid  all  criticism  not  absolutely 
necessary. 

But  I  know  that  Clarke  and  official  science  at  Washing- 
ton, in  and  outside  of  the  Smithsonian  Institution,  will 
immediately  condemn  my  results  for  omitting  this  reduction. 

I  seem  to  hear  that  penetrating  voice,  officially  com- 
manding: 

"  Reduce  to  Emptiness!  Without  Emptiness  and  Vacuity, 
"  there  is  no  Exact  Science,  neither  in  the  Smithsonian 
"  Institution,  nor  in  the  Government  Bureaus. 

u  Reduce  to  Vacuum.     In  Vacuo  Veritas." 

Accordingly,  I  must  take  up  this  subject  also;  for  I  want 
this  value,  As  =  75  exactly,  to  stand,  because  it  is  true. 

The  thesis  referred  to  (p.  22)  and  Clarke  (1.  c.,  p.  215), 


230  ARSENIC. 


give  values  reduced  to  vacuum,  and  base  the  atomic  weight 
of  arsenic  thereupon. 

By  comparing  these  values  with  ours  (the  direct  weigh- 
ings in  air),  it  will  be  seen  that  the  analytical  ratios  reduced 
to  vacuum  are  in 

No.    i          2345          6          7          8        9         10 
31          7         o          7        17          i          i          4         i  i 

low  low  low  low  high  low  low  high  low  low 
compared  to  our  direct  ratios. 

This  shows  that  for  the  first  five  determinations,  in  which 
the  smallest  amount  of  substance  was  used  (less  than  half  a 
gramme),  these  reductions  are  the  largest  and  the  most 
fluctuating,  showing  an  absolute  range  of  48  units  in  the 
fifth  place. 

The  corresponding  fluctuation  in  the  resuJting  atomic 
weight  is  four-thirds  of  a  unit. 

For  the  larger  amount  of  substance  (exceeding  half  a 
gramme)  the  reduction  to  vacuum  is  the  least  and  fluctuates 
least,  the  total  range  being  only  5  units  in  the  fifth 
decimal. 

This  corresponds  to  only  about  0.013  on  the  atomic  weight 
of  arsenic. 

We  notice  plainly  the  enormous  "  high  "  in  No.  5  and 
the  next  in  No.  8,  and  particularly  the  excessive  low  in  No.  i. 

These  results  show  that  in  the  new  Chemical  Laboratory 
of  the  University  of  Pennsylvania,  the  floor  has  already 
begun  to  give  way  very  much,  as  it  did  in  the  laboratory  of 
Stas,  at  Brussels. 

If  the  Stasian  Errors  are  not  definitely  removed  from 
this  new  American  Laboratory,  Professor  Edgar  F.  Smith 
may  next  time  find  himself  several  thousand  yards  down  in 
the  earth — as  did  Stas  in  his  No.  6. 

And  if  Professor  Smith  continues  to  use  the  false  Smith- 
sonian Atomic  Weights  of  Clarke,  in  his  American  Labora- 
tory, I  shall  have  to  leave  him  in  that  hole. 

I  hope  that  Professor  Edgar  F.  Smith  also  will  discon- 
tinue this  humbug  of  reduction  to  vacuum.  See  p.  175. 


EDGAR    F.    SMITH.  23! 


The  cases  above  specified  constitute  a  complete  confir- 
mation of  the  old  opinion  of  Berzelius  concerning  this 
reduction. 

Properly  made,  the  reduction  would  average  about  two 
units  low  in  the  fifth  place.  That  is  the  "gnat,"  in  the 
language  of  Berzelius. 

As  a  matter  of  fact,  I  notice  the  calf  of  a  camel  in  No.  8, 
a  good  sized  camel  in  No.  5,  and  a  big  camel  in  No.  i, 
always  in  the  language  of  Berzelius,  borrowed  by  him  from 
Matthew  XXIII. 

The  determination  made  by  Berzelius  is  often  questioned 
by  recent  chemists — who  ought  to  know  better. 

Thus  J.  G.  Hibbs,  in  his  Thesis  (1896,  p.  21)  criticises 
the  Old  Master  Berzelius,  and  says  he  found  74.840.  As  a 
matter  or  fact,  Berzelius  found  74.95  which  is  much  nearer 
the  truth  than  the  value  given  by  Mr.  Hibbs,  74.9158  with 
the  most  improbable  error  of  0.0022  (pardon  dropping  the 
fifth,  since  the  third  even  is  false). 

We  have  finally  an  inexpressibly  funny  oxidation  method 
by  means  of  potassium  chlorate  and  another  by  means  of 
potassium  bichromate,  both  titrations,  in  the  wettest  of  wet 
ways,  by  Kessler,  1861.  The  first  gave  for  twelve  determi- 
nations the  mean  74  low,  the  second,  one  series,  six  determi- 
nations, mean  55  high,  another  series,  five  determinations, 
46  high. 

The  range  of  the  means  is}  therefore^  129  <(  only." 

This  is  really  too  much  for  me.  I  cannot  put  that  into 
equation,  with  high  and  low  in  the  fifth  place.  I  will  have 
to  put  it,  f rei  nach  Heine,*  melody  by  Stigelli : 

Du  hast  die  Chloratischen  Aetzen, 

Hast  Alles  fur  Saurstoff  begehr, 
Du  hast  ja  Bichromat  Buretten, 

Mein  Arsen,  was  willst  Du  noch  mehr? 


*  Du  hast  Diamanten  und  Perlen 

Hast  Alles  was  Menschenbegehr, 
Ihi  hast  ja  die  schonsten  Augen 

Meia  Liebchen,  was  willst  Du  noch  mehr? 


232  GOLD. 

All  =  197.  GOLD. 

Potassium  Bromo-Aurate,  Ka  Br4  Au  =  556. 

The  compound  was  reduced,  and  the  gold  filtered  off  and 
weighed;  this  is  objectionable. 

The  corresponding  atomic  ratio  is 

Au  :  Ka  Br-Aurate==  197  :  556  =  0.35  432.  Change  n  high. 
Kriiss,  1886,  made  nine  determinations,  the  best  extant  for 
gold. 

Reduction  was  effected  by  SO2  in  Nos.  i,  2,  5,  6,  7;  by 
H  (dry  way)  in  3,  4,  8,  9.  The  mean  of  the  first  is  30  high, 
of  the  latter,  28  high;  hence,  no  great  difference. 

The  mean  of  all  nine  determinations  is  29  high,  corres- 
ponding to  0.26  on  the  atomic  weight. 

But  we  obtain  quite  valuable   indications  by  collecting 

the  results  according  to  the  amount  of  substance  used,  which 

substance  being  dried  over  phosphoric  oxide  without  heat, 

was  the  most  unobjectionable  of  all  employed  up  to  date. 

Aurate,  ab't  10.5   gr.  3  Det.,o.35  474  42  high. 

7.3    «  3  Det.,          457  25  high. 

5-4    "  3  Det.,          453  21  high. 

Extremes:        7.0  gr.          Min.  ratio,        440  8  high. 

10.6    "  Max.  ratio,        476  44  high. 

Total  range :     36. 

Here  we  notice  a  gradual  approach  to  the  atomic  ratio  as 
the  amount  of  substance  diminishes;  the  lowest  individual 
result  is  obtained  with  a  medium  amount  of  substance,  while 
the  highest  was  obtained  by  the  second  largest  amount  used. 

It  is  this  very  marked  effect  of  the  amount,  causing  a 
gradual  approach  to  the  atomic  ratio  as  the  amount  of  sub- 
stance is  reduced,  which  gives  this  work  of  Kriiss  its  value. 
It  plainly  points  the  way,  how  to  proceed  in  a  really  serious 
redetermination.  It  is,  de  facto,  in  accord  with  my  limit 
method. 

Since  o.i  gives  the  ratio  n  high,  we  have  for 
substance,         10.5  7.3  5.4    grammes. 

Au  =  197.38  197.23  197.19 

The  two  extreme  ratios  give : 

Max.  197.40.  Min.  197.07. 


GOLD.  233 

This  shows  plainly  that  a  serious  gradual  approach  to  the 
truth  was  made  with  the  diminution  of  the  amount  of  sub- 
stance used. 

On  the  whole,  the  more  rational  dry  way  reduction 
by  hydrogen  gas  gives  a  mean  2  lower,  and  deserves  the 
preference. 

A  weight  of  about  five  grammes  of  aurate  seems  most 
advisable. 

A  little  further  examination  of  the  results  of  Kriiss,  stated 
on  p.  103  of  Clarke,  shows  that  the  "loss"  supposed  to  be 
Bra  was  low,  37  and  31,  mean  34  in  Nos.  3,  4;  and  9  and  18, 
mean  14,  in  Nos.  8,  9.  The  atomic  ratio  being  0.44  171. 

This  points  to  an  incomplete  reaction  by  the  H,  or  to 
some  lack  of  the  formulated  constitution  in  the  compound. 
Nos.  8,  9  show  smallest  error. 

The  aggregate  of  /oss  with  Au  and  Bra  in  comparison 
with  substance  taken,  show  a  gain  in  Nos.  8  and  9  of  resp. 
6.79  and  2.64  mgr. 

In  No.  3  there  was  a  loss  of  1.28,  in  No.  4  a  gain  of 
0.56  mgr. 

Here  we  are  evidently  touching  a  very  weak  spot  in  this 
work. 

Taking  finally  the  analytical  ratio  Ka  Br  :  Au  of  the 
residue,  and  comparing  the  same  to  the  atomic  ratio  Ka 
Br  :  Au  =  119  :  197  =  0.60  406,  we  find 

Nos.   3489 

405  365  39i  398 

which  is  i  low  41  low  15  low  8  low 

The  last  two,  before  recognized  as  the  best  determina- 
tions, give  the  mean  11.5  low. 

The  following  are  the  conclusions  that  can  be  drawn 
from  this  entire  discussion  : 

I.  While  not  quite  satisfactory  in  results,  this  method 

is  good. 

II.  Needs    careful   repetition,    with   moderate   amount 

(say  5  gr.),  reducing  by  hydrogen,  and 

III.  Checking  results  by  ratio  Ka  Br  :  Au  in  residue. 


234  CLARKE'S  CONFESSION. 


Other  Determinations. 

Thorpe  and  Laurie,  1887,  made,  independently  of  Kriiss, 
a  research  partly  overlapping.  They  subject  the  same  com- 
pound to  reduction  by  direct  heat  (ignition),  which  in  itself 
is  better;  the  residue  was  weighed,  and  gold  determined  by 
washing  out  the  bromide,  and  weighing  the  residue.  They 
thus  give  up  the  original  compound,  on  account  of  their 
impossibility  of  drying  it  completely  without  beginning 
decomposition,  a  difficulty  apparently  overcome  by  Kruss. 

The  low  Brs  in  Kriiss  points  to  some  loss  in  this  direc- 
tion. But  surely,  Thorpe  and  Laurie  obtained  very  inaccu- 
rate results  from  the  residue.  Instead  of  0.60  406  they  found 
the  mean  75  low;  in  this  case,  the  Ka  Br  was  determined  by 
difference  only. 

The  silver  work  of  these  analysts  needs,  of  course,  no 
attention  here. 

The  determinations  of  Mallet,  1889,  have  been  fuHy 
exhibited  in  an  earlier  section  of  this  work.  See  pp.  24-28. 

Clarke  Condemns  His  Own  Work. 

In  this  connection  we  must  quote  the  following  from 
page  ico  of  Clarke's  Constants  of  1897  (we  insert  letters  for 
reference) : 

a  The  former  agreement  between  the  several  series  of 
ft  gold  values  (a)  was  therefore  only  apparent  (b),  and  we 
"  are  now  able  to  see  (c)  that  concordance  among  deter- 
"  minations  may  be  only  coincidence  (d)  and  no  proof  of 
"  accuracy  (e)." 

Our  references: 

(a)  We  did  see  no  such  agreement;  see  diagram,  Plate  I. 
Clarke's  formal  statement  of  fact,  is  false. 

(b)  Was  not  apparent,  was  none  there  at  all. 

(c)  Cannot  see   concordance  of  several  series  or  their 
individual  determinations  yet. 

(d)  Everybody  knew  that  long  ago;  but  we  must  still 
declare  the   absence  of   "  concordance "    in  the   results   of 
Mallet,  as  given  by  himself  and  represented  on  our  diagram 
to  an  exact  scale. 


BARIUM.  235 


(e)  This  is  the  kernel  of  the  whole  matter;  Clarke  con- 
demns himself  most  unequivocally. 

This  is  the  absolute  condemnation  of  the  entire  Clarke 
system  of  combining  all  observations  by  estimating  accuracy 
(weight  of  observations)  by  minuteness  of  probable  errors; 
see  p.  18  and  many  other  places. 

This  whole  system  being,  in  the  above  words  of  Clarke, 
known  to  himself  as  false  and  without  reason,  before  that 
book  of  his  was  published  at  the  expense  of  the  Smithsonian 
Fund  for  the  increase  and  diffusion  or  knowledge  u  per 
orbem  " — every  intelligent  citizen  of  this  country  must  ask 
the  Chief  Chemist  Clarke  this  question : 

(t  If  you  knew  your  entire  system  was  false  in  principle, 
"  how  did  you  dare  issue  it  and  disgrace  American  Science 
"before  the  world?" 

"  Did  you  suppose  your  control  of  the  American  Chem- 
"  ical  Society  would  allow  you  to  '  bluff '  all  efforts  possible 
l<  of  any  chemist  daring  to  expose  your  fraud?" 

Ba=137.  BARIUM. 

Barium  Sulphate,  Ba  O4  S  =  233  and  Barium  Chloride, 
Ba  Ch  —  208,  the  latter  obtained  by  careful  heating  of  the 
crystallized  compound,  are  probably  the  most  stable  and 
fixed  compounds  of  barium.  The  next  in  order  is  Barium 
Nitrate,  Ba  (Oa  N)2=26i,  which  crystallizes  beautifully, 
without  water  of  crystallization.  Lastly  we  have  the  crys- 
tallized chloride,  Ba  Ch  -j-  2  Ha  O  =  244,  also  a  fine,  very 
permanent  compound. 

These  four  compounds  have  been  used  by  eminent 
chemists,  from  Berzelius  and  Turner  to  Struve  and  Marignac, 
for  dry  way  work  in  atomic  weight  determinations. 

The  results  are  not  close,  and  new  determinations,  care- 
fully made,  are  very  desirable. 

The  reactions  are  not  the  best  dry  way  processes,  either ; 
but  the  methods  of  procedure  may  be  improved. 

The  following  is  the  record  of  work  done: 

Ba  O*  S  :  Ba  Cl2  =  233  :  208  =  1.12  019. 

Turner,  1829,  170  high;  Berzelius,  156  high. 

Struve,  1831,        2  Det.    091  —  096.  Mean  75  high. 

Marignac,  1858,  3  Det. ;  032  —  995 ;  37.  "        8  low. 


236 


This  represents  a  very  gradual  approach  to  the  atomic 
ratio,  and  in  the  last  case  the  results  fall  on  both  sides  of 
this  value. 

Ba  (Oa  N)2  :  Ba  O4  S  =  261  :  233  =  1.12  017. 

Turner •,  1833,  3  Det. ;  which  were  41  high,  16  high  and 
29  low,  the  mean  of  which  is  9  high. 

Now,  since  the  mean  of  Marignac  above  was  8  low,  this 
mean  of  Turner  just  about  cancels  it. 

The  two  processes  are  essentially  alike,  the  final  product 
being  the  same,  and  curiously  enough,  the  atomic  ratio  being 
practically  the  same  number. 

This  gives  rise  to  a  peculiar  check  of  which  we  may  have 
something  more  to  say  in  a  near  future. 

2  H2  O  :  Ba  Ch,  2  Hz  0=136  :  244  =  0.14  754. 

Marignac,  1838,  operated  on  2  different  samples,  A  and 
B7  giving 

A,  3  Det.,  800  —  790;  10.     Mean  41  high. 

B,  3  Det.,  810  —  800;  10.         "      49  high. 

Since  now  Ba  1=137.1  gives  the  atomic  ratio  6  low,  this 
would  point  to  Ba  belorv  137,  say  136.2.  The  dehydration, 
therefore,  is  of  little  value,  except  as  to  indicate  that  the 
atomic  weight  is  not  above  137. 

The  first  two  ratios  are  also  rather  dull,  a  change  to  137.1 
lowering  the  ratio  about  6  only.  As  the  analytical  excesses 
were  individually  on  both  sides,  and  for  the  two  processes 
about  equal,  representing  0.15  above  and  below  137,  we 
must  conclude  that  this  value  137  is  proved  by  the  dry  way 
processes  here  enumerated. 

If  Ba=i37.5,  all  these  analytical  excesses  would  be 
increased  considerably,  and  the  results  would  all  be  very  lou\ 

The  wet  way  Silver  Process  has  been  applied  repeatedly 
to  the  Chloride,  and  by  Richards  to  the  Bromide  also.  The 
atomic  ratios  are: 

Ba  Ch    :  Agz  =  208  :  216  =  0.96  296. 
Ba  Br2    :  Aga  =  297  :  216  =  1.37  500. 

Either  of  these  gives  for  137.1  a  rise  of  46. 

For  the  chloride,  Marignac,  in  1848,  found  the  mean  of 
ii  determinations,  64  high.  Dumas,  1860,  16  determina- 


BISMUTH.  237 


tions,  mean  20  high.  Richards,  1893,  14  determinations, 
mean  224  high. 

For  the  bromide,  the  mean  of  15  determinations  oi 
Richards  was  245  high. 

According  to  Richards'  determinations,  we  ought  to  put 
Ba=  137.5. 

We  have  seen  that  this  conflicts  with  the  dry  way  work, 
also  with  Dumas  and  Marignac,  who  would  require  only 
137.05  and  137.15,  or  a  mean  137.1. 

As  the  case  stands,  we  must  conclude  Ba=i37,  until 
positive  dry  way  work,  in  which  definite  compounds  are 
weighed,  proves  that  the  dry  way  work  done  by  Turner, 
Struve  and  Marignac  was  very  badly  done. 


Be  =  9.  BERYLLIUM.  NILSON,  1880. 

The  crystallized  sulphate,  Be  C>4  S,  4  H2  O=  177  yields 
upon  ignition  the  oxide  Be  O  =  25.  The  atomic  ratio  is 
0.14  124,  rise  51  for  o.i. 

Nilson  and  Pettersson,  1880,  made  4  determinations,  from 
52  to  36  high;  mean  45  high. 

Kriiss  and  Mohradt,  1891,  by  the  same  method,  made  16 
determinations,  running  from  37  to  10  high;  mean  20  high. 

The  last  mean  corresponds  to  9.04. 

Bi  =  208.  BISMUTH.  SCHNEIDER,  1851. 

Biz  :  Bi2  Os  =416  :  464  =  0.89  655.  Chg.    5  low. 

Schneider,  1851,       8  Det.,  682  —  634;  48.       Mean    o  low. 
Marignac,  1883,       6  Det.,  696  —  658;  38.          "      27  high. 
Lowe,  2  Det.,  656  —  640;  16.          u        7  low. 

Schneider,  1894,  6  Det.,  662 —  648;  14.  "  2  high. 
Bi2  (O*  S)3  :  Bi2  Oa  =704  :  464=  1.51  724.  Chg.  20  low. 
Marignac,  1893,  6  Det.,  775  —  682;  93.  Mean  4  high. 
This  record  is  sufficient.  Schneider's  work,  of  1851, 
determined  the  value;  Marignac  by  his  new  method  con- 
firmed it;  Schneider,  in  1894,  settled  the  question.  We 
have  no  room  for  rubbish. 


238  BROMINE. 


Bo=11.  BORON.  RAMSAY,  1893. 

We  have  given  all  necessary  data  and  methods  very  fully 
in  Part  III,  pp.  141-159. 

We  may  add  the  determination  by  water  of  crystallization 
of  borax  on  account  of  its  historical  interest  (compare  pp. 
42-44)  Borax  =  Naz  O?  Bo4  -\-  10  H2  O. 

Water:  Borax  ==  180  :  382  =  0.47  120. 

Berzelius,  1826,    3  Det.  Mean  10  low. 

Laurent,  1849,       2  Det-  "       55  high- 

Hoskyns-Abrahall,  1892 : 

5  Det.,  230  high;  87  high.  "     167  high. 

Ramsay  and  Aston,  1893 : 

7  Det.,    83  high ;  10  low.  "      48  high. 


Br  =  80.                             BROMINE.               MARIGNAC,  1843. 

Br  :  Ag  =  8o  :  108  =  0.74  074.              Change  93  high. 
Marignac,  1843,          3  Det.,  072  —  055;  17.     Mean  3  high. 

Stas,  1865,                    i  Synthesis. 

ft 

9  low. 

Stas,  1865,                    4  Det.,  083  —  079;    4. 

ft 

7  high. 

Wet  Way  Titrations  : 

Huatington,  1881,       6  Det.,   in  —  035;  76. 

<t 

3  low. 

Richards,  1890,           6  Det.,  076  —  044;  32. 

tt 

9  low. 

Richards,  1893,         n  Det.,  089  —  034;  55. 

tc 

7  low. 

These  three  series  were  made  in  connection  with  deter- 
mination of  Cd,  Cu,  Ba. 

Other,  perfectly  concordant  determinations  by  Cooke 
(Sb),  Thorpe  (Ti),  Thorpe  and  Laurie  (Au)  can  only  be 
mentioned. 

It  will  be  noticed,  that  Marignac-Huntington,  and  Stas- 
Richards'  (2)  exactly  balance. 

The  atomic  weight  of  bromine  has  long  been  known 
to  be  exactly  commensurable  to  that  of  silver,  namely, 
Br  :  Ag  =  So  :  108  =  20  :  27. 

All  other  work  done  is  either  not  direct  or  has  been 
properly  placed  in  the  Chemische  Rumpelkammer. 

We  have  no  space  for  either  here. 


CADMIUM.  239 


C       12.  CARBON-DIAMOND.  DUMAS,  1840. 

All  necessary  data  given;  see  p.  39  and  pp.  101-105. 
Ca      40.  CALCIUM. 

All  necessary  data  given;  see  pp.  106-108. 

The  work  is  not  as  concordant  as  required  for  so  impor- 
tant an  element. 

Critical  research  on  the  methods  used  have  been  carried 
on  for  some  years  and  will  be  completed  by  actual  final 
determinations  as  soon  as  time  shall  permit. 

Cd       112.  CADMIUM.  v.  HAUER,  1857. 

Cd  S  :  Cd  O4  8=144  :  208  =  0.69  231.  Chg.  15  high. 

1  Karl  v.  Hauer,  1857,    9  Det.,  257 —  209548.    Mean  o  high. 

2  Partridge,          1890,  ioDet.,2O5  — 185520.       "    32  low. 
Cd  :  Cd  O  =  112  :  128  =  0.87  500.  Chg.  10  high. 

3  Morse  and  Jones,  1892 : 

10  Det.,  508  —  504;     4.      Mean     7  high. 

4  Lorimer  and  Smith : 

9  Det.,  518  —  491;  27.          "        4  high. 

5  Bucher,  1894,         2  Det.,  511 — 504;     7.          "        8  high. 

6  Bucher,  1894,        3  Det.,  491  —  484;     7.          "       13  low. 

7  Morse  and  Arbuckle,  1900,  Absorption  of  Oxygen? 

3  Wet  Way.     4  Electrolysis.     5  Porcelain  Crucibles,  both. 

6  Pt  Cr.  in  Porcelain  Crucible. 

Cd  O  :  Cd  O*  C2  —  128  :  200  =  064  °°O-  Chg-  J8  high. 

8  Lenssen,  1860,    3  Det.,  053  —  982;  71*.     Mean  10  high. 

9  Partridge,  1890, 10  Det.,  971— 957;   14.         "       36  low. 
10    Morse  and  Jones,  1892 : 

5  Det.,  008  — 996;  12.        "        3  high. 
14    Bucher,  1895,       8  Det.,  014  —  951;  63.        "      22  low. 

M.  and  J.  finding  subst.  slightly  hygroscopic,  took  neces- 
sary precautions;  hence,  probably  "9"  higher. 
Cd  S  :  Cd  O4  C2  =.  144  :  200=20.72  ooo.          Chg.  14  high. 

12  Partridge,  1890,  10  Det.,  979  —  968;  n.     Mean  27  low. 

13  Bucher,  1895,     10  Det.,  065 — 037;  28.         "      51  high. 
No.  i,  Standard;  No.  2,  some  error;  Nos.  3,  6,  reason- 


240  CHLORINE. 


able,  give  corresponding  atomic  weight  below  112.1.     Oxa- 
late-Work,  Nos.  8  to  13,  inferior,  as  might  be  expected. 
Electrolysis,  Hardin,  1896: 

14  Cd  :  Cd  Ch,      10  Det.,  252  —  236;     16.  Mean  42  high. 

15  Cd  :  Cd  Br2,      10  Det.,  210  —  196;     14.       "       27  high. 

By  Silver: 

16  Cd  Ch,  Dumas,  1860: 

6  Det.,  083  —  618;  465.      "     121  high. 

17  Cd  Br2,  Huntington,  1881  : 

8  Det.,  110  —  045;     65.       "     150  high. 
B  y  Silver  : 

18  Cd  Ch,  Bucher,  1895: 

21  Det.,  949  —  880;     69.       "     153  high. 

19  Cd  Bra,  Huntington,  1881  : 

8  Det.,  437  —  405;     32.      «      82  high. 

20  Cd  Bra,  Bucher,  1895: 

5  Det.,  480  —  453;     27.       "     124  high. 
These  results   speak  for   themselves.     Even  electrolysis 
not  satisfactory;  but  both  silver  processes  worthless. 


CERIUM. 

The  following  two  reactions  have  been  preferred  by 
chemists: 

2  Ce  O2    :  Ce2  (O4  S)a  and  2  Ce  O2    :  Cea  (Ca  O4)a 
The  results  are  still  unsatisfactory. 

Ratio:                    A,  Sulphate.  B,  Oxalate. 

Ce  =  139                     0.60  429  0.63  loo 

HO                              563  235 

141                               702  370 

Difference  per  unit     139  135 

A.  Brauner,  1885,  23  Det,  604  —  549;  55.      Mean  0.60  573. 

B.  Buehrig,  1875,    5  Det.,  0.63  432. 
Possibly  Ce  =  140. 

CI-35.5.  CHLORINE.  TURNER,  1833. 

See  pp.  97-101. 

The  various  Stasian  Reactions  have  been  disposed  of  in 
the  preceding,  and  are  fully  reviewed  in  my  True  Atomic 
Weights;  they  have  finally  been  thrown  into  the  Rumpel 
Kammer. 


CHROMIUM. 


24I 


Co  =  59?  COBALT. 

Co  :  Co  O  =  59  :  75  =0.78  667.  Change  28  high. 

1  Russell,  1863,  14  Det,  614 — 550;  64.  Mean  75  low. 

2  Zimmermann,  1886,  10  Det.,  638  —  630;    8.       "     32  low. 

3  Kriiss, 

4  Remmler,  1891,         24  Det,  859  —  508  5351 .       "     54  low. 
2  Co  :  Co2  Cl«,  ION  H3=u8  :  501=0.23  553.  Chg.  30  high. 

5  Sommaruga,  1866,       7Det.,858 — 806;  52.  Mean  274  high. 

6  Lee&W.Gibbs,i87i,6Det,587  — 569;  18.        "     27  high. 

In  4  gradual  fractioning,  Oxide  points  to  o.i  low;  but 
purpureo-cobalt  chloride  points  to  as  much  high.  If  both 
substances  equal  in  value,  Co  =  59. 

Cr  =  52.  CHROMIUM. 

Cr2  Oa  :  Am2  OT  Cr2=i52  :  252=0.60  318.  Chg.  31  high. 

1  Rawson,  6  Det.,  368  —  330;  38.     Mean  28  high. 

2  Meinecke,  1891,        5  Det,  353  —  320;  33.        "       14  high. 
Cr2  Oa  :  Ag2  O?  Cr2=i52  :  432=10.35  185.     Chg.  30  high. 

3  Berlin,  1846,  i  Det.,  121  high. 

4  Sievert,  1861,  2  Det,  262 — 139;  123.     Mean    16  high. 
Cri  Oa  :  2  Ag  O*  Cmi52  :  664=0.22  892.     Chg.  23  high. 

5  Berlin,  1846,  4  Det.,  Mean  122  high. 

6  Sievert,  1861,  Shows  why  high. 

7  Meinecke,  1891,      6  Det,  943  —  924;  19.       Mean  39  high. 

These  are  the  only  determinations  worth  consideration ; 
the  final  product  is  the  sesquioxide,  obtained  by  ignition. 
They  suffice  to  fix  the  unit. 


Cs=133. 


CESIUM. 


Cs  Cl  :  AgCl  =  168.5  :  H3-5  — I-I7  421.     Chg.  70  high. 

1  Johnson  &  Allen,  1863, 4  Det,  580 — 399;  181.  Meati78high. 

2  Bunsen,  1863,  3  Det,  503— 435;    68.       "    46  high. 

3  Godefroy,  1876,  4  Det.,  265— 107;  158.       "  257  low. 

Bunsen's  mean  corresponds  to  133.06. 
But  since  only    the    silver    chloride   process  has  been 
employed,  this  result  is  not  final. 


242 


=  63.5  COPPER. 

Blue  Vitriol  =  Cu  O4  S,  5  Hz  O  =  i.oo  ooo 


gives  atomic  ratios : 
Loss:  H2  O  ==0.36072 

"       H 2  O-f  SO 3=0.68  136 


Cu  O4  8—0.63  928 
CuO  =0.31  864 
Cu  =0.25  451 


1  Richards,  1891,  Cu  by  electrolysis.     4  low,  i  high,  3  high. 

H2  O  heat  5  high,  5  high. 

Detail,  True  Atomic  Weights,  1894;  p.  132. 
Cu  :  Cu  0  =  63.5  :  79.5  =  0.79  874.         Chg.  25  high. 

2  Erdmann  and  Marchand,  1844: 

3  Det.,  878  — 860;  18.    Mean    2  low. 

3  Millon  and  Commaille,  1863: 

3  Det.,  791  —  770;  21.        "     95  low. 

4  Hampe,  1873,  3  Det.,  838  — 831;     7.        "      39  low. 

5  Richards,  1891,          2  Det.,  820  —  802;  18.         "      63  low. 

Richards  (5)  is  in  conflict  with  (i) ;  but  Erdmann  and 
Marchand  (2)  are  in  concord. 

It  is  of  course,  understood  that  Professor  Richards  finds 
quite  another  value  for  copper,  and  how  he  succeeds  in  doing 
so  we  have  shown  in  our  True  Atomic  Weights,  1894,  pp. 
128-136;  also,  before  that  time,  in  Zeitschrift  f.  Anorg. 
Chemie,  Bd.  v.,  pp.  293-298;  1893,  and  in  Chemical  News, 
Oct.  6,  1893. 

It  is,  as  in  the  case  of  Crookes :  The  work  is  there,  but 
tangled  up  with  errors  of  all  kinds ;  we  have  unraveled  the 
tangle  and  showed  the  analysts  what  the  results  of  their 
work  really  is. 

Fe=56.  IRON.  SVANBERG,  1844. 

All  necessary  data  given,  pp.  91-95. 


19.  FLUORINE.  LOUYET,  1849. 

Ca  O4  S  :  Ca  Fh  =  136  :  78  =  1.74  359.  Chg.  446  low. 
Record  to  4  places  only  :  1.74  36.         "       45  low. 

Berzelius,  1826,  Fluorite,  3  Det.,  1.750.  "      64  low. 


FLUORINE.  243 


Louyet,  1849,  Fluorite,  6  Det.  Mean  1.7437,  i  high. 
Artif.  3  Det.  "  i-74i7>  19  low. 

De  Luca,  1860,  Fluorite,  4  Det.          "      1-7459;  23  high. 

Dumas,  1860,      Fluorite,  i  Det.          "      1-7455?  19  high. 

Moissan,  1890,  2  Det.       No  data  given. 

Naz  O4  S  :  2  Na  Fl  =  142  :  84=  1.69  048.  Chg.  402  low. 

Record  to  4 places  only  :  1.69  05.       cf         40  low. 

Louyet,  1849,  3  Det-     Mean  1.6847,  58  low. 

Dumas,  1860,  2  Det.         "      1.688,    25  low. 

Moissan,  1890,  5  Det.     No  data  given. 

Ka2  O4  S  :  2  Ka  Fl=i74  :  116=1.50  ooo.    Chg.  258  low. 

Record  to  4  places  only  :  1.5000.  "       26  low. 

Dumas,  1860,  2  Det.     Mean  1.4991,    9  low. 

Ba  O4  S  :  Ba  Fl3=233  :  175  =  1.33  143.     Chg.  152  low. 

Record  to  4  places  only  :  1.33  14.        Chg.     15  low. 

Louyet,  1849,  3  Det.     Mean  1.331,      4  low. 

Moissan,  1891,  2  Det.     No  data  given. 

It  is  to  be  regretted  that  the  determinations  of  Moissan 
cannot  be  used,  he  having  failed  to  give  any  direct  weigh- 
ings. See  p.  35. 

The  principal  data  are  those  of  Louyet,  who  lost  his  life 
on  account  of  this  work.  It  is  sufficient  to  establish  Fl  =  19. 
On  account  of  the  low  value,  four  decimals  are  perfectly 
sufficient. 

By  the  value  given  for  the  change,  the  analytical  excess 
stated,  give  for  Louyet's  determinations,  from  Fluorspar 
18.999,  from  the  sodium  salt,  19.15  and  from  the  barium 
compound,  19.025.  As  the  pure  fluorite  is  probably  the 
purest,  the  standard  19  is  the  true,  absolute  value  within  the 


H  =  1  HYDROGEN. 

This  atomic  weight  is  commonly  taken  as  unit.     But  it  • 
cannot  be  taken  as  standard,  for  hydrogen  cannot  be  weighed 
with  precision,  being  a  gas. 

We  have  said  sufficient  on  the  questions  here  involved, 
especially  in  our  True  Atomic  Weights.  It  will  incidentally 
be  shown  here  also. 


244  LORD    RAYLEIGH. 


The  same  is  true  to  the  exact  value  of  this  atomic  weight 
in  reference  to  that  of  oxygen ;  see  True  Atomic  Weights, 
pp.  177-183  on  the  determinations  of  Dumas,  and  pp. 
185-189  on  determinations  bj  Keiser,  Morley,  Ditmar  and 
Julius  Thomsen. 

Lord  Rayleigh's  Determinations. 

The  most  important  work  on  hydrogen  we  have  inciden- 
tally given  on  page  162,  in  the  density  determinations  by 
Lord  Rayleigh,  namely,  H  =  1.0028  for  O  =  16  exactly. 

An  earlier  determination  by  the  same  authority  is  1.0062; 
see  p.  161.  This  was  in  1893,  before  the  discovery  of  argon. 
The  above,  much  smaller  value  was  obtained  after  this  dis- 
covery, which  incidentally  increased  the  experience  in  this 
work  very  greatly. 

We,  therefore,  may  conclude  H  =  1.0028  to  represent  an 
upper  limit  for  hydrogen. 

This,  the  most  difficultly  purified,  most  difficultly 
retained  pure  gas,  shows,  in  the  hand  of  this  master,  a 
density-atomic  weight  of  1.006  in  1893,  and  only  1.003  in 
1897. 

We  conclude  that  the  true  atomic  weight  of  absolutely 
pure  hydrogen  is  i.ooo,  to  which  Lord  Rayleigh  approached 
within  0.006  in  1893,  and  to  within  half  that  limit  (0.003)  *n 
1897. 

Every  impurity  necessarily  raises  the  density  of  this,  the 
lightest  of  all  gases. 

Morley's  Determinations. 

The  most  pretentious  work  of  Morley  on  hydrogen,  has 
appeared  since  the  publication  of  our  work  of  1894.  It  was 
(C  recommended  for  publication  by  F.  W.  Clarke,"  and  pub- 
lished in  grand  style  by  the  Smithsonian  Institution  as  No. 
980  of  its  <{  Contributions  to  Knowledge,"  in  1895. 

I  do  not  deem  it  necessary  to  enter  upon  the  "  complete 
syntheses"  of  water  by  Morley;  for  this  element,  it  is  pre- 
ferable to  use  density  determinations,  as  for  nitrogen.  We 


HYDROGEN.  245 


have  not  time  to  look  into  the  many  more  numerous  errors 
possible  in  that  synthesis. 

Ed-ward  W.  Morley  is  a  thorough  Stasian — with  all  that 
implies;  he  glories  in  it.  We  can  take  space  only  for  a 
very  few  particulars. 

Being  also  very  Clarkian,  he  aims  above  all  at  minute 
"probable  errors;"  that  is,  de  facto,  close  concordance. 
He  shapes  his  work  with  a  special  view  of  this  requirement. 

This  is  desirable,  within  certain  restrictions;  but  it  is  the 
height  of  folly  to  suppose  that  mere  concordance  is  truth.  We 
have  shown  that  repeatedly. 

Morley's  Show  of  Precision. 

Morley  makes  a  wonderful  show  of  precision.  This  often 
is  fatal.  For  example,  he  gives  full  record  of  weight  com- 
parisons (p.  31)  for  1887  and  1892;  to  eight  decimals  for  the 
gramme  set,  to  five  decimals  for  the  milligramme  set. 

He  does  not  give  deviations  merely;  that  would  look  too 
simple  and  would  be  practical.  No,  he  gives  complete 
numbers. 

Thus,  his  lo-gr.  piece,  in  1887,  was  38,  in  1892,  only  8 
hundredths  mgr.  light. 

He  puts  this  9  999.62  and  9  999.92  which  looks  impres- 
sively exact  to  the  common  chemical  public,  but  would  be 
too  ridiculously  cumbrous  for  actual  use. 

It  is,  of  course,  curious  to  note  that  this  ten-gramme 
piece  gained  in  weight  by  use  during  five  years. 

The  loo-gr.  piece  was  short  66  and  49  hundredths  mgr. 
in  1887  and  1892,  but  the  5O-gr.  3  short  in  1887,  and  36  long 
in  1892. 

Wonderful  precision — suspiciously  so,  when  stated  that 
the  weights  have  been  little  used  and  handled  with  great 
care. 

It  might  have  proved  interesting  to  have  such  u exact" 
determinations  made  at  shorter  intervals.  The  changes  are 
too  funny. 

But  we  have  room  only  for  the  results  of  his  weighings 
of  hydrogen  and  oxygen,  expressed  in  grammes  per  liter 
(his  density). 


246  WEIGHING    OF 


Weighings  of  Oxygen. 

For  oxygen  he  made  three  series  of  weighings  according 
to  as  many  methods.  He  gives  his  results  to  5  places.  We 
will  leave  them  at  that;  but  add  the  extremes  and  range  to 
the  means. 

Mean.  Extremes.  Remarks. 

I.  9  Det.,    1.42  879          907  —  838;     69. 

II.  9  Det.,  890          952  —  853;     99.  "globes" 
6  Det.,            869          880  —  851 ;     29.  «  globe  3  " 
All  15,     1.42  887 

III.  7  Det.,  918          957  —  860;     97.    from  chlorate. 
10  Det.,  908          951 — 849;  102.       "    electrolys. 
All  17,      1.42  917 

Morley  gives  the  probable  error  of  these  three  means  to 
the  millionth  of  the  gramme,  of  course.  We  will  give  them 
to  the  fifth  decimal;  they  are  claimed  to  be  3,  5,  5  in  the 
fifth  place,  that  is,  the  last  decimal  given  above. 

But  even  if  these  were  the  probable  errors  of  the  means, 
they  would  invalidate  the  fifth  decimal. 

As  a  matter  of  fact,  we  see  the  third  decimal  changes! 
But  let  us  continue  to  talk  in  theyf/?^,  as  above  printed. 

We  find  that  the  mean  for  "  globe  3  "  is  21  less  than  for 
"  globe  5."  But  21  in  fifth  place  amounts  to  £  or  two-tenths 
of  a  milligramme  ! 

To  what  is  this  change  due?  To  any  thing  about  the  gas? 
Oh,  no! 

The  gas  weighed  is  the  same ;  but  it  does  not  weigh  the 
same,  because  it  is  contained  in  a  different  glass  globe! 

But  don't  Morley  allow  for  the  weight  of  his  glass  globes? 
Surely,  he  does,  with  the  utmost  precision,  and  gives  the 
fuW  data  on  pp.  29  and  30. 

Why  then  this  difference?  Well,  that  is  just  the  trouble 
with  our  Stasian  exact  chemists,  such  as  Morley. 

They  are  so  exact — oh,  it  is  absolutely  wonderful  to  read! 

And  when  they  get  through,  some  strange  error  stares 
them  in  the  face,  for  which  they  cannot  account. 

They  may  strain  at  the  gnats — but  the  camel  they  cannot 
hide,  although  they — don't  mention  him. 


OXYGEN.  247 


In  fact,  the  above  little  "  camel  "  -whom  we  found  roaming 
about  in  the  wilderness  of  Morley's  figures,  is  not  mentioned 
by  Morley. 

Yet,  on  results,  claimed  exact  to  the  fifth  decimal,  hav- 
ing on  the  mean  only  a  probable  error  of  5  units  in  the  fifth, 
we  detect  a  difference  of  21  units  in  the  fifth  between  the 
MEANS  of  six  determinations  made  in  "globe  3"  and  nine 
determinations  made  in  "  globe  5."  This  difference  bet-ween 
the  means  is  over  four  times  the  amount  of  the  probable 
error  of  the  mean  of  all  15  determinations,  and  amounts  to 
two-tenths  of  a  milligramme. 

But  two-tenths  of  a  milligramme  is  a  quantity  of  com- 
mon recognition  in  all  good  chemical  analysis. 

Now,  why  does  not  Morley  show  up  this  great  conflict 
of  the  means  according  as  his  oxygen  was  weighed  in 
"  globe  3  "  or  "  globe  5,"  the  weight  of  which  was  properly 
and  minutely  allowed  for? 

Possibly  he  did  not  notice  this  little  camel;  he  was  too 
busy  straining  at  gnats.  At  any  rate,  he  does  not  say  any- 
thing about  it. 

We  notice  next,  that  the  oxygen  from  chlorate  was  o.i 
mgr.  heavier  per  litre  than  the  electrolytic  oxygen. 

We  notice  that  the  third  series  gave,  in  both  of  its  divis- 
ions, a.  full  milligramme  difference  between  the  lightest  liter 
and  the  heaviest  liter. 

But  a  milligramme  is  a  full  grown  camel,  when  the  gnats, 
are  given  to  the  hundredth  of  the  milligramme^  and  the 
"probable  error"  are  gnats  of  the  thousandth  of  a  milli- 
gramme. 

In  first  division  of  Series  II,  the  range  is  also  99-100, 
that  is,  a  full  milligramme.  In  the  first  series  it  is  %  of  a 
milligramme. 

What  must  we  conclude  from  these  facts?  That  the 
work  of  Morley  is  so  wonderfully  exact  as  Clarke,  and  the 
Secretary  of  the  Smithsonian,  and  the  Stasian  Ostwald,  and 
the  admiring  members  of  the  American  Association  or  the 
American  Chemical  Society  are  expected  to  believe  and 
vociferously  do  believe? 

Is  not  this  "credo"  of  exact  science  shamefully  ridiculous? 


248  WEIGHING     OF 


We  can  not  afford  to  take  conclusions  ei  ready  made'*  by 
authorities  at  Washington  or  at  Berlin;  we  have  to  be 
convinced  by  the  facts,  and  not  by  the  apparent  forms  of 
accuracy  and  the  official  dictum. 

And  seeing,  that  the  means  of  a  liter  of  oxygen  actually 
vary  to  the  extent  of  £  mgr.  according  as  it  is  contained  in 
one  or  another  globe; 

and  seeing,  that  the  weight  of  a  liter  of  oxygen  is  de  facto 
varying  to  a  full  milligramme  in  different  determinations  in 
three  series  (II  first,  III  first  and  second)  ; 

ive  must  admit  these  facts  as  the  true  limit  of  the  accuracy 
attained, 

although  Mr.  Morley  may  imagine  that  he  has  attained 
to  the  precision  of  his  " probable  error"  of  one-twentieth  of 
the  milligramme! 

Morley  has  determined  the  -weight  of  a  liter  of  oxygen  with 
an  uncertainty  of  one  milligramme  at  best  in  any  one  of  these 
series. 

But  how  much  is  this  weight,  to  the  nearest  milligramme  ? 

Why,  that  is  rather  uncertain,  again.  Let  us  see.  We 
will  give  both  Morley's  own  means,  and  ours  rounded  off  at 
the  proper  place. 

Weight  of  One  Liter  of  Oxygen,  in  Grammes. 


Morley.       "Rounded  off."    Determinations. 

Series      I 

1.42  879 

1.42  88 

9 

"        II 

887 

89 

15 

"      III 

917 

92 

17 

Mean    1.42  9  41 

We  notice  a  distinct  and  gradual  increase  in  the  weight, 
from  the  first  to  the  last  series  of  Morley;  the  total  change 
amounting  to  almost  half  a  milligramme. 

These  are  the  actual  scientific  results;  the  "fifth"  deci- 
mal is  imagination,  pure  and  simple. 

Morley's  Weighings  of  Hydrogen. 

We  must  next  consider  Morley's  weighings  of  hydrogen. 

He  gives  his  results  to  the  millionth  of  the  gramme  per 
liter;  that  is  the  thousandth  of  the  milligramme. 

Wonderful,  truly  wonderful,  is  the  precision  of  Morley's 
work — on  paper. 

Turning  to  page  63,  where  the  19  determinations  of  his 


HYDROGEN.  249 


second  series  (made  according  to  his  second  method)  are 
recorded,  we  find :  Grammes. 

No.  17  0.089  869 

No.  18  0.090  144 

These  two  consecutive  determinations,  made  when 
Morley  had  gained  experience  in  making  16  determinations 
preceding  in  this  series,  and  all  15  determinations  of  the  first 
series,  differ  by 

o.ooo  275  grammes. 

This  is  2f5  millionths  of  a  gramme,  or  0.275  of  a  milli- 
gramme; over  a  quarter  of  a  milligramme! 

But  when  consecutive  determinations  differ  by  almost 
three  tenths  of  a  milligramme — what  is  the  use  of  giving  us 
thousandths  of  the  milligramme? 

This  is  either  humbug  or  fraud,  unless  it  be  a  contemptible 
mixture  of both ;  tit's  Stasian. 

We  conclude  that  the  weighings  to  the  thousandths  of 
the  milligramme  are  simply  for  show,  and  for  fooling  the 
members  of  the  American  Association  and  of  the  American 
Chemical  Society. 

We  shall  have  room  for  only  a  complete  summary  of  his 
five  series,  but  shall  express  the  results  in  milligrammes  for 
convenience.  We  shall  not  drop  any  of  his  fine  work,  for 
the  thousandth  of  a  milligramme  is  just  the  same  as  the 
millionth  of  the  gramme. 

Morley:     Weight,  in  mgrs.,  of  liter  of  hydrogen. 

Series]     I        15  Det.,  993  — 846;  147.        Mean  89.838 

"        II        19  Det.,  144  — 869;  275.  "  970 

"      III          6  Det.,  912  —  856;  056.  "  886 

«      IV*        6  Det.,  972 -777;  195.  «  880 

«        V        n  Det.,  883 -830;  053.  «  866 

Mean  of  all         57  Det.,  144  — 777;  367.  "      89.873 

The  means  are  those  actually  given  by  Morley,  in  which 

a  final   little  gnat  of  one  thirty-thousandth  was  allowed 

for  (see  his  p.  28),  which  amounts  to  3  units  in  the  last 

decimal  here  given,  that  is  to 

one-third  of  a  hundredth  of  a  milligramme  ! 

*  The  extremes  of  this  series  are  put  by  Morley  in  brackets  [  ] 
commonly  used  to  indicate  their  exclusion  from  consideration. 

Being  rather  greatly  divergent,  our  friend  of  concordant  results 
naturally  desires  to  suppress  these  results.  But  he  fails  to  give  any 
reason  for  this  exclusion.  Hence  we  must  keep  them,  as  Morley's  own 
fine  determinations. 


250  EFFECT    OF 


Looking  at  the  above  tabulated  means  as  given  by  Morley 
himself,  we  recognize  the  utter  folly  of  such  a  "  correction," 
except  for  show  of  an  exactness  NOT  attained  to  in  fact. 

For  we  see  readily,  that  the  longer  Mr.  Morley  kept 
weighing  hydrogen,  the  lighter  it  became,  precisely,  as  our 
corresponding  table  for  oxygen  showed  plainly  (though  we 
did  not  accentuate  it  in  words)  that  oxygen  grew  heavier  on 
his  hands,  the  longer  he  kept  weighing  it.  See  p.  248. 

Suppose,  for  a  moment,  that  Mr.  Morley  had  not  stopped 
weighing  these  two  gases — would  that  be  any  reason  for  the 
hydrogen  ceasing  to  grow  lighter? 

I  should  not  think  so;  of  course,  Morley  weighing  with 
utmost  exactness,  can  not,  and  therefore  has  not  erred — 
except  in  ceasing  to  weigh  altogether. 

We  shall  resume  this  fascinating  subject  further  on. 

We  must  first  obtain  the  mean  weight  of  a  liter  of  hydro- 
gen, according  to  the  exquisitely  accurate  weighings  of  Mr. 
Morley,  made  to  the  thousandth  of  the  milligramme. 

But — that  is  absolutely  impossible,  the  weight  is  not 
irregularly  varying,  but  varies  gradually  and  steadily. 

Ah,  indeed!  That  is  the  trouble.  Morley  has  got  it. 
Of  course  he  was  liable  to  catch  it.  Indeed,  he  is  afflicted 
with  Morbus  Stasii,  very  badly. 

Let  us  drop,  therefore,  that  humbug  of  the  thousandths 
of  a  milligramme.  We  have  shown  it  to  be  a  humbug 
here — as  we  have  in  other  cases. 

We  shall  have  all  the  uncertainty  we  want  to  touch  with 
these,  our  hands,  if  we  round  off  the  above  results  of  Morley 
to  the  hundredth  of  a  milligramme. 

Dropping  the  Thousandths  of  the  Milligramme. 

Mean  weight  of  a  liter  of  hydrogen  in  mgrs. 

Series      I          15  Det.,  99  —  85;  14.          Mean  89.94 

"         II          19  Det.,  14  —  87;  27.              "  97 

"       III            6  Det.,  91—86;     5.              «  89 

"       IV            6  Det.,  97  —  78;  19.              «  88 

"         V          1 1  Det,  88  —  83;     5-              "  87 


PRACTICE.  251 


Combining,  we  obtain 

Series  I,  II          34  Det.,   14 —  85529.  Mean    89.95 

"      III,  IV,  V         23  Det.,  14  —  78 ;  36.  88 

Mean  of  all,  57  Det.,   14  —  78536.  "        89.91 

Actual  extremes  are : 

Highest,  Series   II.        90.14  mgr. 
Lowest,         «     IV.        89.78    " 
Absolute  Range,  0.36    te 

The  actual  range  of  the  weights  of  one  liter  of  hydrogen 
is,  therefore,  a  little  over 

one  third  of  a  milligramme, 

which  is  exactly  one  hundred  times  the  weight  of  the  last 
gnat  strained  out  by  Morley.    Page  249,  supra. 

Of  course,  such  straining  may  strain  the  strongest  man. 
It  has  affected  Mr.  Morley  seriously  and  induced  the  Morbus 
Stasii. 

But  we  must  close  this  subject.  We  shall  here  give  the 
general  mean  of  all  determinations,  the  extreme  means  of  a 
single  series,  and  the  actual  extremes  of  the  entire  work. 

Weight  of  Liter  in  Mgr.  Hydrogen.  Oxygen. 

Absolute  lowest,  89.78  1428.3 

Lowest  mean,  89.87  1428.8 

Mean  of  all,  89.91  1429.0 

Highest  mean,  89.97  1429.2 

Absolute  highest,  90.14  1429.6 

Absolute  Range,  0.36  1.3 

Uncertainty,  one  in  250  1 100 

These  are  the  actual  facts.  The  total  range  actually 
covered  does  not  necessarily  include  the  truth.  We  remem- 
ber, that  almost  all  coins  actually  weighed  were  light — so 
also,  all  -weight  of  a  liter  of  a  given  gas  may  be  either  light 
or  heavy j  as  compared  to  the  actual  range  of  weight,  accord- 
ing as  there  may  lurk  a  trace  of  a  lighter  or  heavier  gas,  in 
the  supposedly  pure  gas  ! 

Now,  we  do  know  heavier  gases  that  no  means  of  purifi- 
cation used  by  Morley  could  have  removed — such  as  argon. 
On  burning  the  hydrogen  to  water,  the  argon  would  remain 
dissolved  in  the  water,  under  the  exact  conditions  used  in 
Morley's  complete  synthesis  of  water. 


252  RATIO    O  :  1 6. 


But  we  have  not  time  nor  space  to  enter  upon  that  subject 
now. 

Morley's  Ratio  0:16. 

Let  us  divide  the  actual  weight  found  for  a  liter  of  oxy- 
gen by  16,  the  standard  atomic  weight  of  oxygen;  the 
quotient  will  be  the  weight  of  our  liter  of  oxygen  per  unit  of 
atomic  weight. 

This  weight  must 'be  compared    to   the   weight  actually 
found  by  Morley  for  a  liter  of  hydrogen, 
i  Liter  of:          Oxygen.       -^  Oxygen.     Hydrogen.     Excess. 
Lowest,  1428.3  89.27  89.78  0.51 

Mean,  1429.0  89.31  89.91  0.60 

Highest,  1429.6  89.35  90.14  0.79 

All  weights  in  milligrammes. 

We  see  that  hydrogen,  according  to  Morley's  weighing, 
exceeds  the  sixteenth  part  of  the  weight  of  oxygen  by  from 
0.5  to  0.8  a  milligramme  per  liter. 

It  is  not  constant,  this  excess,  because  the  actual  uncer- 
tainty in  the  weight  of  hydrogen  is  one  in  250  and  of  oxygen 
one  in  noo  only;  that  is,  oxygen  is  weighed  with  4  to  5 
times  the  precision  attained  for  hydrogen. 

The  data  given  in  our  table  (p.  251),  plainly  show  that 
the  uncertainty  for  hydrogen  is  a  little  less  than  one-half  of 
one  per  cent,  while  for  oxygen  it  is  less  than  one-tenth  of 
one  per  cent. 

Accordingly  we  might  well  accept  the  sixteenth  of  the 
weight  of  oxygen  as  a  more  reliable  determination  than  the 
directly  weighed  hydrogen. 

As  a  matter  of  fact,  Morley  left  an  uncertainty  of  0.36 
mgr  or  over  ^  of  one  milligramme  in  the  weight  of  one  liter 
of  hydrogen. 

This  is  but  a  very  little  less  than  the  actual  difference 
between  the  weight  of  a  liter  of  hydrogen  and  the  one-six- 
teenth of  the  weight  of  a  liter  of  oxygen. 

Compare  General  Chemistry,  1897,  p.  378. 

Can  these  results  of  Morley  be  taken  as  positive  experi- 
mental demonstration  that  O  :  H  is  not  16:1? 

When  Lord  Rayleigh  found  "  atmospheric  "  nitrogen  a 


RATIO  o  :  16.  253 

trifle  "  high "  did  he  conclude  the  Laws  of  Nature  to  be 
false? 

No ;  he  suspected  some  heavier  gas  present  as  an  impurity 
that  had  escaped  the  reagents  used  for  purification. 

He  tried  to  isolate  it,  and  discovered  argon. 

Does  Morley's  hydrogen  contain  a  trace  of  argon  ?  What 
is  it  that  causes  this  slight  difference  in  weight,  almost 
covered  by  the  actual  uncertainties  of  weighing  brought 
out  by  us? 

Is  it  simply  due  to  errors  of  handling  and  weighing  of 
hydrogen?*  Let  us  remember  that  Morley  found  oxygen 
much  heavier  in  "globe  5  "  than  in  "globe  3." 

Probably  that  is  all.  At  any  rate  no  certain  difference  of 
the  atomic  weight  by  hydrogen  has  been  established  by 
Morley  from  the  value  of  the  sixteenth  of  that  of  oxygen. 

Morley  says  his  gases  were  pure  ;  yet  he  reports  having 
found  CO?,  N,  etc.,  in  these  pure  gases,  and  that  he  don't 
know  how  they  got  there ! 

Morley's  Ratio  0 :  H. 

We  want  to  obtain  the  ratio  of  oxygen  to  hydrogen,  and 
also  the  value  of  hydrogen  for  oxygen  taken  at  16. 

According  to  Morley,  the  first  is  15.879;  this  has  been 
"  adopted"  by  the  Chief  Chemist  and  made  the  basis  of  his 
Smithsonian  System  of  Atomic  Weights  (Constants  of 
Nature,  1897,  p.  33). 

Therefore,  it  is — taken  as  true  by  all  official  chemists  of 
the  United  States  and  by  the  American  Chemical  Society. 

But  is  this  really  the  expression  of  Morley's  determina- 
tions? 

Oh,  not  at  all,  as  every  one  familiar  with  the  determina- 
tion of  the  QUOTIENT  of  two  experimental  data  knows.* 

*This  professional  blunder  is  most  remarkable,  since  nearly  all  com- 
mon works  on  quantitative  research  give  specific  directions  on  this  point. 

See  Kohlrausch's  Leitf  aden,  IV  ed.,  1880,  p.  7-9,  which  treats  this  very 
case  of  the  error  of  a  quotient,  such  as  a  specific  gravity  determination. 

The  simplest  is  my  method  in  my  Elements  of  Physics,  1870,  p.  12. 

The  corresponding  condition  in  Ostwald's  Hand  und  Hilfsbuch,  1893, 
p.  4,  last  case,  is  not  fulfilled,  for  O  is  over  four  times  as  accurately 
determined  as  H.  See  p.  252. 


254  RATIO   o  :  H. 


If  we  have  several  determinations,  can  we  take  simply 
the  quotient  of  the  means  ? 

Hardly.  In  the  present  case,  we  found  even  the  means 
changing  during  the  progress  of  the  work  of  Morley. 

His  oxygen  became  gradually  heavier,  his  hydrogen 
gradually  decidedly  lighter;  see  pp.  248  and  250. 

Accordingly,  the  ratio  O  :  H  has  grown  greater  as  Morley 
became  more  expert  by  practice. 

If  Morley  had  kept  up  the  work,  there  is  no  telling  how 
much  this  ratio  would  have  grown. 

Let  us  see,  as  to  his  means. 
Earliest  Series  : 

Oxygen,  Series      I  1428.79     mgr. 

Hydrogen     "        II  89.97       " 

giving  the  ratio  O  :  H  =  15.881 
and  for  O  =ri6  exactly,  H  =  1.0075. 

Last  Series: 

Oxygen,  Series  III  1429.17     mgr. 

Hydrogen,  «         V  89.87       " 

giving  the  ratio  O  :  H  =  15.902 

and  for  O  =  16  exactly,  H  —  1.0061. 

Here  we  have  an  actual  increase  of  the  ratio  from  15.88 
to  15.90  and  a  corresponding  diminution  of  the  atomic 
weight  of  hydrogen  from  1.008  to  1.006,  stopping  at  the  third 
place. 

Now  if,  on  the  means,  Morley  gradually  weighed  oxygen 
so  much  heavier  and  hydrogen  so  much  lighter,  that  he 
reduced  the  excess  of  the  atomic  weight  from  8  to  6  thou- 
sandths, how  long  would  he  have  had  to  keep  training  and 
improving  in  skill,  to  reduce  this  excess  to  nothing,  and 
prove  H  =  i  exactly? 

We  shall  not  undertake  to  answer  this  question. 

But  we  shall  again  turn  to  the  actual  results  of  Morley. 
This  time  the  absolute  extremes  will  be  called  for. 

It  is,  of  course,  understood  that  we  dare  not  touch  one  of 
these  determinations  of  Morley.  They  are  made  by  a  mas- 
ter, all  of  them.  Sometimes  the  very  extremes  are  nearest 
the  truth,  as  we  have  repeatedly  found. 


RATIO    O  !   H.  255 


Hence,  let  us  see  what  the  extremes  teach  us 
Oxygen,  highest,  1429.6        mgr. 

Hydrogen,  lowest,  89.78        " 

giving  the  ratio  O  :  H  =  15-923 

and  for  O=  16  exactly,  H  =  1.0048. 

Oxygen,  lowest,  1428.3        mgr. 

Hydrogen,  highest,  90.14        " 

giving  the  ratio  O  :  H  —  15.846 

and  for  O  =  16  exactly,  H  =  1.0098. 

The  actual  determinations  by  Morley,  therefore,  range 
as  follows : 

Atomic  Weight 

For  Oxygen.  Ratio  O  :  H.  H,  for  O  =  16. 

Absolute  lowest,  15.846  1.0098 

Mean,          "  15.881  1.0075 

Mean  of  all,  J5-894  1.0067 

Mean  highest,  15.902  1.0061 

Absolute  highest,  i5«923  1.0048 

This  is  the  true  expression  of  the  actual  determinations 
made  by  Morley. 

We  may  here  repeat  the  values  obtained  by  Lord  Ray- 
leigh ;  see  p.  244. 

Hydrogen,  for  O  =  16,  exactly. 
1893  1.0062 

1897  1.0028 

It  seems  to  us  that  Morley  has  been  doing  reasonably 
well ;  if  he  only  had  kept  up  his  practice,  he  might  again 
have  halved  his  smallest  value  and  come  up  to  the  level  of 
Lord  Rayleigh,  in  1897. 

Within  the  range  of  Morley's  determinations  of  the 
weights  of  a  liter  of  oxygen  and  of  hydrogen,  he  has 
obtained  results  ranging 

for  H,  from  1.0098 
to  1.0048 

the  excess  above  i  having  ranged  from  98  to  48  ten-thou- 
sandths, which  is  the  same  as  from  ten  to  five-thousandths. 
How  much  longer  would  he  have  had  to  practice,  to  drop 
the  other  half  of  his  original  excess? 


256  HOPEFUL    PROGRESS. 

At  the  same  time,  the  ratio  O  :  H  ran  up  from  15.85  to 
15.92  or  seven-hundredths. 

How  much  longer  would  Mr.  Morley  have  had  to  practice 
to  gain  another  such  seven-hundredths,  and  prove  the  ratio 
15.99  which  is  no  doubt  near  the  true  16.00? 

Morley's  Hopeful  Progress. 

Judging  from  the  very  notable  progress  Mr.  Morley  made 
in  this  direction,  it  must  be  regretted  that  he  stopped  prac- 
ticing so  soon. 

But  we  doubt  very  much  whether  Mr.  Morley  would  have 
been  able  to  accomplish  this  work.  His  aim  was  simply 
concordance,  as  required  by  Clarke. 

He  never  tried  to  find  the  true  value;  for  he  cannot  admit 
the  possibility  of  constant  errors,  he  is  too  much  affected 
by  Morbus  Stasii,  complicated  with  a  very  natural  develop- 
ment of  Furor  Clarkii. 

But  we  have,  in  our  examination  of  his  results,  shown  up 
several  notable  cases  of  aggravated  acerberations  of  Morbus 
Stasii. 

For  example,  the  fact  that  his  gas  was  intrinsically 
heavier  in  one  globe  than  in  another,  he  did  not  notice  any 
more  than  Stas  became  aware  of  the  floor  of  his  laboratory 
sinking  four  thousand  yards  with  him  when  reducing  his 
silver  nitrate  No.  6  to  vacuum. 

We  have  said  enough  about  this  whole  investigation. 

It  has  been  the  expressed  ambition  of  Mr.  Morley  to 
emulate  Stas.  I  am  sure  he  has  succeeded  admirably. 

The  results  of  Stas  will  have  to  be  hunted  up  in  the 
Chemical  Rumpelkammer. 

The  larger  part  of  the  work  of  Morley  will  be  found  in 
the  same  place — close  by  the  work  of  Stas. 

The  Stasians  have  imitated  their  master  and  teacher  in 
calling  every  chemist  not  accepting  their  doctrine,  a  vis- 
ionary, depending  upon  imagination,  and  believing  in 
chimeras. 

We  have  pulled  the  lion  skins  from  the  animals  parading 
as  great  chemists,  most  excellent  and  accurate  workers, 
unexcelled  in  precision. 


STATE    SCIENCE. 


257 


The  first  reaction,  when  deprived  of  that  false  wrap,  has 
been  a  lusty  bray:  extrapolation,  selection,  imagination. 
Then  have  come  misrepresentation  and  actual  fraud. 
We  will  leave  them  at  that  stage  to  their  own  meditation. 

State  Science  and  State  Church. 

By  reference  to  pp.  47-49  and  p.  187  of  my  True  Atomic 
Weights,  of  1894,  every  chemist  can  see  how  courteously  I 
treated  Messrs.  Clarke  and  Morley. 

Drunk  with  power,  and  full  of  the  false  notion  of  experi- 
mental exactness,  they  have  acted  as  brutes,  at  meetings  in 
Washington,  Madison,  and  in  their  publications. 

I,  therefore,  have  had  no  reason  to  state  the  case  other- 
wise than  regard  to  scientific  truth  requires. 

It  is  a  most  deplorable  fact  that  the  General  Government 
has  gone  into  the  building  up  of  a  Science  Trust  of  the  most 
formidable  character,  now  using  nearly  ten  million  dollars 
a  year. 

STATE  SCIENCE  is  already  now  showing  greater  corrup- 
tion and  demoralization  than  STATE  CHURCH  could  boast  of 
after  a  thousand  years  of  power  in  all  Christendom. 

When  the  most  famous  of  the  branches  of  State  Science 
at  Washington,  namely,  the  Smithsonian  Institution,  pub- 
lishes as  true  and  highest  science  a  work  so  unspeakably 
corrupt  in  every  fiber  as  the  so-called  Constants  of  Nature 
of  Clarke,  with  its  falsehood-page  6,  it  is  impossible  to  use 
language  strong  enough  to  condemn  this  system. 

There  is  just  as  much  reason  for  our  Government  to  take 
in  hand  the  building  up  of  a  National  Religion,  as  it  can 
find  for  its  actual  building  up  of  a  National  Science  at  the 
lavish  expenditure  of  millions  of  dollars  a  year. 

Is  there  any  pressing  necessity  for  our  Government 
building  up  an  Academy  of  Laputa  at  Washington,  such  as 
Gulliver  describes? 

Hg  =  200.  MERCURY.  E  RDM  ANN.  1844. 

The  necessary  details  have  been  given,  pp.  95-96,  for 
the  oxide,  pp.  96-97  for  the  sulphide,  and  pp.  97-99  for  the 
chloride.  See  also  bromide  and  cyanide,  p.  100. 


258  IODINE. 


In -113.5.  INDIUM.  WINKLEfl.  1867. 

Iri2  :  Iti2  Os  =  227  :  275  =  0.82  546.      Change  13  high. 
Winkler,  1867,  3  Det.,  581 —  537;  44.     Mean  10  high. 

Bunsen,  1870,  i  Det.,  589.         "       43  high. 

The  radio-tests  of  Benoist  (C.  R.  132,772;  1901),  confirm 
it  to  be  a  sesquioxide. 

The  work  of  Winkler  needs  being  confirmed.  His  two 
gold-substitutions 

In  :  Au=  113.5  :  J  97  =  0-57  614 

gave  values  rather  high,  namely,  208  high ;  but  we  know  that 
this  process  cannot  give  accurate  results. 

10  =  1 27.  IODINE.  MARIGNAC,  1 842. 

Ka  lo  :  Ag  =  166  :  108—  1.53  704.      Change  92  high. 
Marignac,  1842,        5  Det.,  ^94 —  651;  143.     Mean    5  low. 

This  corresponds  to  only  0.005  on  Iodine. 

Clarke  (1897,  p.  48),  says  this  work  of  Marignac  was 
"without  remarkable  accuracy."  The  range  is  rather  high, 
but  the  mean  is  all  right,  and  that  is  what  Clarke  always 
wants;  even  his  own  probable  error  of  this  mean  is  only  18 
in  our  units;  but  that  corresponds  to  0.02  only  on  the  atomic 
weight,  which  ought  to  be  good  enough. 

Ag.  lo  :  Ag  =  235:  108  =  2.17  593.      Chg.   92  high. 
Marignac,  1842,        3  Det.,  519  —  500;  19.        Mean  59  low. 
Stas,  1865?  a,  2  Det.,  536  —  529;     7.  "      60  low. 

b,  6  Det,  543  —  530;  13.  "      56  low. 

c,  5  Det.,  539  — 529;  10.  "      60  low. 
Since  Clarke  has  pleased  to  throw  his  reproach   upon 

Marignac,  we  here  take  these  determinations  from  the 
Rumpel  Kammer,  to  show,  that  Marignac's  work  was  equal 
to  that  of  Stas,  as  even  Clarke  has  to  admit  (1.  c.,  p.  49). 

All  these  determinations  are  about  60  low,  which  repre- 
sents 0.06  low  on  the  atomic  weight  of  iodine,  as  readily  seen. 

Ir       193.  IRIDIUM. 

Ir  :  Ka2  Cl«  Ir  =  193  :  484  =  0.39  876.       Chg.    12  high. 
Seubert,  1978,  8  Det.,  890  =  868;  22.        Mean    4  high. 

The  corresponding  Ammonium  Salt  gave  values  67  high 
in  mean,  but  deserve  less  credit. 

For  192.5,  the  atomic  ratio  is  0.39814. 


LITHIUM.  259 


Ka      39.  POTASSIUM. 

Ka  Oa  N  :  Ka  Cl  =  101  :  74.5  =  1.35  570.     Chg.  47  low. 

Penny,    1839,  Ser.    I,  7  Det.,  640 —  630;   10.   Mean  66  high. 

II,  7  Det.,  641— 628;  13.        «    63  high. 

Stas,  1865,  7  Det.,  655  —  638;  17.       "    75  high. 

Hibbs,  1896,  5  Det.,  642 — 620522.        "     57  high. 

These  give  in  this  order,  014,  0.13,  0.18  and  0.12  high. 
Stas  gives  39.18,  Hibbs  39.12. 

The  method  is  one  used  in  the  vicious  circle  of  Stas,  and 
is  unfit  for  anything. 

But  we  have  no  real  direct  determinations  for  potassium, 
confined  to  oxygen  compounds. 

La.  LANTHANUM. 

La2  Os  :  Laa  (O4  8)3  =326  :  566  =  0.57  598.  Chg.  14  high. 

These  values  result  from  the  common  La  139.  The 
following  is  the  analytical  record : 

Hermann,  1861,        3  Det.,  690  —  610;    80.     Mean    57  high. 
Zschiesche,  1868,      6  Det.,  277  — 745;  532;        "      576  low. 
Cleve,  1874,  5Det.,  667  — 590;    77.        "       22  high. 

"       1883,  12  Det.,  500  — 458;     42.        "      117  low. 

Brauner,  1882,  2  Det.,  566  —  549;     17.        "       39  low. 

"        1882,  5  Det.,  525  — 451;     74.        "      1 17  low. 

Bauer,  1884,  406^,569  —  482;     87.        "        73  low. 

These  are  apparently  the  best  determinations  for  this 
element;  they  show  plainly,  that  the  final  work  has  not  yet 
been  commenced. 

Li  =  7.  LITHIUM. 

CO2  :  LiaOa  0  =  44  :  74  =  0.59  460.     Change  162  low. 
Diehl,  1862,  4  Det.,  440  —  401;  39.        Mean    43  low. 

Troost,  1862,  2  Det.,  485  — 427;  58.  "          4  low. 

The  value  of  Troost  would  be  only  0.002  high,  or  7.002 ; 
but  the  range  is  too  great. 

The  other  determinations  belong  mainly  to  the  Stas  mud- 
dle.   We  give  briefly,  first  our  atomic  ratio ;  also  R  =  range. 
0.29  617,  Li  Cl  :  Ag  Cl,    Mallet,  2  Det.,  R  56.  Mean  27  low. 
Troost,  2  Det.,  R  45.       "     24  low. 

0.39  352,  Li  Cl  :  Ag,         Stas,      3  Det.,  R   5.       "6  high, 
i  .62  353,  Li  Oa  N :  Li  Cl,  Stas,      3  Det.,  R  12.       "  242  high. 


26O  NITROGEN. 


Mg  =  24.  MAGNESIUM.     SCHEERER,  1850. 

See  pp.  108-115  for  a  full  exposition  of  all  that  is  essential. 

Mn  =  55.  MANGANESE. 

Mn  O  :  Mn  O4  8  =  71  :  151  =0.47  021.     Chg.  35  high. 
Marignac,  1883,          4  Det.,  032  —  987;  45.     Mean  14  low. 
Weeren,  1890,  6  Det.,  005 — ooo;     5.        l(      19  low. 

Ag+MnO  :  AgCU  Mn  =  179  :  227  =  0.78  855.  Chg.  9  high. 
Dewar  and  Scott,  1883 : 

6  Det.,  917  —  756;  161.     Mean  20  low. 

These  are  the  least  objectionable  methods  on  chemical 
reasons.  The  second  shows  in  execution  great  range  and  is 
atomically  dull;  the  analytical  excess  represents  over 0.2  low. 

This  leaves  the  work  of  Marignac  and  Weeren,  giving  a 
departure  of  about  0.05  low. 

Mo  =  96.  MOLYBDENUM. 

Mo  :  Mo  03=96  :  144=10.66  667.     Change  23  high. 
Dumas,  1859,  Reduct,  6  Det.,  741 — 4955  24^  Mean  18  low. 
Deb  ray,  1868,       "       3  Det.,  604  —  5035101.       "     in  low. 
Rammelsberg,  1877,  Reduct,  i  Det.,  "      41  high. 

Seubert  and  Pollard,  1895 : 

Reduct,  5  Det.,  679  — 661;    18.      "        i  high. 

2  Na  Cl  :  Na2  O*  Mo=:  117  :  206  =  0.56  796.     Chg.  27  low. 
E.  F.  Smith  and  Maas,  1893 : 

10  Det. ,760  —  733527.     Mean  51  low 

The  work  of  friend  Edgar  F.  Smith,  done  by  Maas,  is 
very  good,  giving  Mo  only  0.2  high.  But  the  direct  reduc- 
tion process,  in  Seubert's  laboratory,  gives  the  identical 
absolute  value;  only  0.004  high  as  limit. 

N  =  14  NITROGEN.      LORD  RAYLEIGH,  1895. 

This  most  important  determination  is  fully  exposed,  pp. 
159-168. 

The  ojd  Stasian  work  on  this  atomic  weight  is  shown  up 


SODIUM.  26l 


on  pp.  169-198,  and  the  last  folly  on  this  topic  is  presented 
pp.  169-209. 

The  determinations  of  Julius  Tfiomsen,  of  Copenhagen 
(Oversigt  pp.  342-355;  1893),  have  been  used  by  Clarke 
(1897,  69),  and  called  u valuable"  for  nitrogen;  hence  we 
must  consider  them  here,  though  they  were  made  for  the 
ratio  O  :  H. 

H  Cl  :  Ha  1^  —  36.5  :  17  =  2.14  706.      Chg.  1256  low. 

Series        I  n  Det.,  160  —  030;  130.     Mean  613  low. 

"  II  5  Det.,  130  — 067;     63.        "      614  low. 

"         III  2  Det.,  094  — 08 1 ;     13.        "      618  low. 

We  see  here  the  Stasio-Clarkian  demand  of  concordance 
to  be  the  sole  aim;  the  range  is  reduced  from  130  to  13. 
But  the  constant  error  remains  practically  the  same,  and 
amounts  to  about  0.55  on  N,  making  it  N=  14.05. 

Of  course,  if  the  process  is  correct,  it  must  apply  equally 
well  for  O  or  N  (see  pp.  144-147). 

But  the  process  is  not  good  (p.  54),  and  conflicts  with 
the  rule  and  spirit  of  Berzelius,  who  seems  to  be  forgotten 
in  Denmark.  Compare  p.  84. 

Na  =  23.  SODIUM.  Mrs.  ASTON,  1893. 

The  determination  of  boron  by  Ramsay  and  Aston,  in 
1893,  we  have  utilized  for  a  truly  crucial  determination  of 
boron,  which  we  have  credited  to  Ramsay,  and  an  excellent 
determination  of  Na  which  is  credited  to  Mrs.  Aston. 

The  precision  is  certainly  within  o.oi.     See  pp.  147-148. 

The  only  other  process  that  needs  consideration  is  the 
following: 

Na2  O4  S  :  Na2  Os  C  =  142  :  106  =  1.33  962.  Chg.  64  low. 
Richards,  1891,         8  Det.  005  —  950;  55.        Mean  23  high. 

The  range  represents  0.086  on  the  atomic  weight,  and  the 
analytical  excess  23  high  represents  0.036  low  on  the  atomic 
weight,  making  it  22.964. 

We  see  that  this  work  of  Richards  would  be  strongly 
confirmatory,  if  such  volumetric  work  had  any  great  weight 
at  all.  Incidentally,  this  shows  how  badly  all  calculations 
of  Richards  are  muddled  and  off. 


262  PHOSPHORUS. 


Ni  =  58.  NICKEL, 

The  most  promising  salt  to  be  used  appears  to  be  the 
double  salt  Kaz  O*  S-fNi  O*  S  -f-  6  H2  0  =  436.  Unfor- 
tunately Sommaruga,  1866,  resorted  to  the  Barium  Sulphate 
process : 

Ni  Salt:  Ba  O4  S  =436  :  466  =  0.93  562.  Chg.  22  high. 
He  made  six  determinations ;  654  —  645 :  9.  Mean  89  high, 
corresponding  to  Ni  =.  58.4. 

Ni  :  Ni  O  =  58  :  74  =  0.78  378.  Change  29  high. 

The  analytical  excess,  from  Russell,  1863,  to  Kriiss  and 
Schmidt,  1892,  has  been  brought  down  from  215  high  to  66 
high;  but  this  last  still  represents  0.3  on  the  atomic  weight, 
high! 

0  =  16  OXYGEN. 

This  value  is  determined  by  Dumas,  1840;  for  we  take 
Diamond-Carbon  as  our  Standard  of  Matter  (Comptes 
Rendus,  T.  117,  pp.  1075-1078;  1893,  and  True  Atomic 
Weights,  1894,  pp.  174-175). 

Since  for  O  =  16  we  found  C  =  12  exactly,  it  follows  that 
adopting  C  12  exactly,  we  obtain  O=i6  by  the  same  set 
of  determinations. 

Osn=191  OSMIUM. 

Seubert,  in  1888,  made  use  of  the  Chloro-Osmiates  of 
Ammonium  and  of  Potassium;  the  reaction  is  atomically 
dull,  a  change  of  only  about  12  for  one-tenth  unit  on  the 
atomic  weight  of  osmium. 

In  his  second  paper,  the  ammonium  salt  gives  the  mean 
analytical  excess  47  high,  the  potassium  salt  74  low. 

Hence,  the  former  points  to  0.4  high,  the  latter  to  0.6  low. 

All  we  dare  say  is  that  191  will  probably  prove  the  true 
value. 

P      31.  PHOSPHORUS.       SCHROETTER,  1851. 

P2  Os  :  p2  =  142  :  62  =  2.29  032.  Chg.  420  low. 

Schroetter,  1851,         10  Det.,  300 — 783;  517.  Mean  113  low. 
Van  der  Plaats,  1885,   2  Det.,  201 — 072;  129.       "     104  high. 
Mean  of  both  series,       "        5  low. 


PALLADIUM.  263 


Schroetter  corresponds  to  31.027;  V.  d.  P.  to  30.975;  the 
mean  is  31.001. 
0.05  741.     P2  Agio: 

V.  d.  Plaats,  1885,  737  —  726;  13.     Mean    9  low. 
°-77  327«    Ag3  :  Ag3  O4  P: 

V.  d.  Plaats,  1885,  326—300;  26.        "       14  low. 
0.42438.     PCl3:3Ag: 

Dumas,  1860,          469  —  444;  25.         (C       17  high. 

Pb     -207.  LEAD.  BERZELIUS.   1810. 

This  is  the  first  atomic  weight  established  with  care  and 
precision,  by  the  father  of  chemical  symbols,  chemical  lan- 
guage and  atomic  weights. 

See  this  book,  Part  II,  Chapter  II,  pp.  74-91. 

Pd=  106.5?  PALLADIUM. 

Pd  :  Pd  CU  Kaz  =  106.5  :  326.5=0.32  619.     Chg.  20  high. 
Berzelius,  1828,  2  Det.,  Mean  70  high. 

Joly  and  Leidie,  1893,  3  Det. : 

Rejected  by  authors,  used  by  Clarke. 
"      "        "        1893,  4  Det.,  Mean  164  low. 

"      "        "        1893,  2  Det,  ««       138  low. 

Pd  :  Pd  (N  Ha,  Cl) 2=106.5  :  211.5=0.50  355.  Chg.  24  high. 
Reiser,  1889,  Ser.     I      n  Det.,  383— 344;    39.  Mean  5  high. 
«      II       8  Det.,  382-343;    39.       «      4  high. 
Bailey  and  Lamb,  1892, 10  Det.,  218— 088;  130.       "  184  low. 
Keller  and  Smith,  1892,   9  Det.,  519 — 502;    17.       "  153  high. 
Ser.     I  4  Det.,  422— 350;    72.      "    30  high. 
«      II  6  Det.,  388— 360;    28.      "     19  high. 
u    III  4  Det.,  430—401 ;    29.      "    59  high. 
Keiser  and  Breed,  1894: 

Ser.      I  5  Det.,  356— 339;    17.      "      4  low. 
"      II  4  Det.,  360-345;    15.      "     i6high. 
W.  L.  Hardin,  1900,  uses  Diphenyl-Pd-diammon,  Cl  and 
Br,    also    Am     Br-Palladate.     Claims    Pd=K>7.     Fresen. 
Ztschr.,  Bd.  39,  p.  541 ;  1900. 

The   result  points  to   106.5,   which  we   might  adopt  if 


264  SULPHUR. 


Reiser's  other  determinations  had  not  shown  so  remarkable 
fluctuations,  as  in  regard  to  hydrogen. 
But  the  conflicts  are  too  great. 

Pt=195.  PLATINUM.  SEUBERT,  1881. 

See  the  excellent  analytical  determinations  of  Seubert  in 
Part  III,  pp.  115-119. 

Rb  85.5?  RUBIDIUM. 

Rb  Cl  :  AgCl=i2i  :  143.5=0.84  321.     Chg.  69  high. 
Bunsen,  1861,  4  Det.,  388 — 175;  213.     Mean  68  low. 

Piccard,  1862,  406^,313  —  245;    68.        "      31  low. 

Godeffroy,  1876,       4  Det,  354  — 320;     34.         "       14  high. 

The  master  came  within  o.i;  hence,  no  use  to  credit  the 
value  to  the  closer  work  of  15  years  later. 

Other  determinations  are  called  for,  independent  of  this 
silver  process. 

Rh=103?  RHODIUM. 

Rh  :  RhCh  (N  £13)5=103  :  294.5=0.34  975.     Chg.  22  high. 
Seubert  and  Kobbe,  1890 : 

10  Det.,  974  —  929;  45.     Mean  21  low. 
This  is  the  only  series  of  value,  known  to  me.    The  work 
done  under  Seubert,  probably  permits  the  value  103  to  be 
taken. 

Ru-  102?  RUTHENIUM. 

Ru  :  Ru  O'2  =  102  :  134  =  0.76  119.     Change  18  high. 
Joly,  1889,  4  Det.,  075  —  046;  29.     Mean  59  low. 

This  corresponds  to  101.7.  All  other  work  is  objection- 
able and  very  meager.  New  and  serious  work  is  demanded. 

S  =  32.  SULPHUR.  MARCHAND,  1844. 

Set  pp.  96-97  for  the  fundamental  determinations,  which 
here  are  supplemented  with  some  of  the  more  interesting 
direct  determinations. 

Ag2  S  :  Ag2  =  248  :  216=1.14  815.        Chg.    14  low. 
Dumas,  1860,          5  Det.,    838  —  811;  27.        Mean    8  high. 
Stas,  1865,  5  Det.,    854  —  8495    5-  "      37  high. 

Cooke,  1877,     I    5  Det.,    892  — 882;  10.  "      73  high.* 

Ill    2  Det.,    823  — 810;  13.  "      15  high. 

*  Rejected  for  cause. 


ANTIMONY.  265 


See  True  Atomic  Weights,  1894,  p.  98.  Series  I  of  Cooke, 
highly  concordant,  but  greatly  in  error,  because  silver  lost 
by  volatilization,  as  Cooke  found  himself.  He  instituted  the 
third  series  under  special  conditions,  avoiding  such  loss; 
hence  he  properly  rejected  Series  I,  as  we  do,  and  retained 
III  only.  The  second  series  was  also  rejected,  for  same 
reasons;  in  third  series  reduction  took  place  without  visible 
glow. 

We  should  have  stated,  that  Dumas  and  Stas  operated  by 
actual  synthesis,  while  Cooke  reduced  pure  sulphide  in  a 
current  of  hydrogen. 

Ag2  :  Ag2  O4  S  — 216  :  312=0.69  231.     Chg.  20  high. 
Struve,  1851,  6  Det.,  244  —  212;  32.        Mean    i  low. 

Stas,  1865,  6  Det.,  209— 197;  12.  "     28  low. 

Both  series  were  reductions  in  a  current  of  hydrogen. 
Struve  used  from  5  to  12  grammes  of  Sulphate,  Stas  from  56 
to  83  grammes.  The  observations  of  Cooke  explain  the 
difference  in  the  results. 

I  do  not  think  there  will  remain  a  single  result  of  all  the 
much  lauded  work  of  Stas  after  ten  years. 

Sb  =  120.  ANTIMONY.  SCHNEIDER,  1856. 

Sa  :  Sba  Sa  =96  :  336  =  0.28  571.  Chg.  16  low. 
Schneider,  1856,  8  Det.,  559 — 481 ;  78.  Mean  51  low. 
Cooke,  1877,  ii  Det.,  "  53  low. 

Schneider,  1880,        3  Det.,  546  —  534;  12.          "      30  low. 

Schneider  reduced  pure,  crystallized  Stibnite,  from  Arns- 
berg;  minute  impurities  of  Ca  Carbonate  and  Fe  Sulphide 
were  allowed  for.  Cooke's  work  was  synthetic,  in  wet  way 
mainly.  Schneider's  last  value  represents  120.2. 

The  work  is  very  difficult. 

While  reading  the  final  proof  I  received  from  Professor 
Edgar  F.  Smith  his  recent  determinations  made  by  heating 
tartar  emetic,  dried  at  150°,  in  a  current  of  dry  muriatic 
acid,  leaving  pure  potassium  chloride.  How  the  carbon  is 
disposed  of,  need  not  here  be  stated,  except  that  evidently  a 
slight  loss  of  the  chloride  can  hardly  be  avoided;  hence  we 
expect  the  analytical  ratio  to  come  out  low. 


266  ANTIMONY. 


KaO  Sb,  C4  H4  06  —  323,  Ka  €1  —  74.5;  hence, 
Chloride  :  anhydr.  Tartrate  =  o.23  049.         Change  10  low. 

Aided  by  G.  C.  Friend,  eight  determinations  were  made, 
ranging  from  041  to  049,  and  from  24  to  16  low;  mean  ana- 
lytical excess  17.3  low,  corresponding  to  Sb  =  120.17. 

Accordingly,  this  result  agrees  with  the  chemical  estimate 
of  the  process  (ratio  low,  hence  atomic  weight  high). 

It  is  a  valuable  process,  and  deserves  to  be  worked  with 
great  care. 

It  is  very  much  to  be  regretted  that  only  the  values 
reduced  to  vacuum  are  given  (see  pp.  229-230) ;  we  cannot 
rely  except  on  direct  weighings. 

I  am  much  obliged  to  Professor  Smith  for  fhe  reprint 
(from  Journal  American  Chemical  Society,  XXIII,  502-505 ; 
July,  1901),  kindly  sent  me. 

Of  course,  since  Prof.  Smith  uses  the  false  atomic  weights 
of  Clarke,  he  finds  Sb—  120.353;  since  he  spares  us  the 
probable  error,  we  will  overlook  the  third  decimal. 

The  false  Clarke  auxiliaries  just  doubles  the  error  of  this 
work  of  E.  F.  Smith. 

The  other  determinations  will  be  given  in  our  abbreviated 
form;  our  atomic  ratio  standing  first;  R  signifies  range. 
Electrolysis : 
1.25  984,  Sb2  :  Cua,  Pfeifer,  1881 : 

3  Det.,  R    36.     Mean  2275  high. 
o-37  037,  Sb  :  Ags,  Pfeifer,  1881 : 

7  Det.,  R  171.         «      448  high. 

o-37  037>  Sb  :  A§3-  Popper, : 

15  Def,  R  253.         «      397  high. 

Silver  Processes,  gravimetric  determinations : 
0.63  830,  Sb  Bra  :  3  Ag  Br,  Cooke,  1877 : 

15  Det.,  R  188.         "          o 
0.71  064,  Sb  loa,  Cooke,  1877, 7  Det.,  R  209.       "          4  low. 

Titrations:  Dexter,  1857;  Dumas,  1859;  Kessler,  1861 — 
lead  to  Sb  122,  generally  received  till  1877.  Bongartz,  1883, 
takes  the  cake  for  absurdities;  published  in  Berichte  D. 
Chemische  Gesellschaft. 


SILICON. 


26* 


8e=79. 


SELENIUM.         PETTERSSON,  1877. 


Se 


Se  02  =  79:  111=0.71  171.  Chg.  26  high. 
Sacc,  1847,  3  Det.,  161 — 102 ;  59.  Mean  83  low. 

Ekman&Pettersson,  1876,  7  Det.,  199—185 ;  14.     "      20  high. 

Ag2  :  Ag2  Oa  Se  =  2i6  :  343  =  0.62  974.  Chg.  iSlow. 
Ekman&Pettersson,  1876,  7  Det.,  o£x — 93x5  50.  Mean  17  low. 
Hg  :  HgSe  =  200  :  279  =  0.71  685.  Chg.  59  low. 
Erdmann  and  Marchand,  1852 : 

3  Det.,  741 — 726;  15.  Mean  48  high. 

All   other   determinations  without  value.     In  the  above 
cases,  the  limit  of  precision  is  about  o.i  on  the  atomic  weight. 


Si  =  28. 


SILICON. 


THORPE,  1887. 

Chg.     24  high. 


Si  O2  :  Si  Br4=6o  :  348  =  0.17  241, 
Thorpe  and  Young,  1887 : 

9  Det.,  368  —  324';  44.   Mean  106  high. 

Si  CU  :  4  Ag=  170  :  432  =  0.39  352.  Chg.     23  high. 

Pelouze,  1845,  2  Det.,  457  —  433 ;  24.    Mean    93  high. 

Dumas,  1860,  3  Det.,  411 — 340571.         "       25  high. 

Si  Ch  :  4  Ag  Cl  =  170  :  574  =  0.29  6*17.  Chg.      17  high. 

Schiel,  1861,  2  Det.,  633  —  592541.    Mean     4  low. 

We  credit  the  determinations  to  Thorpe,  because  of  the 
method,  giving  the  oxide  which  is  weighed  as  such;  the 
substance  is  unsatisfactory,  and  the  result  too  wide  of  mark, 
0.4.  The  problem  is  very  difficult  and  not  settled. 


Sn       118. 


TIN. 

:    118  = 


Sn  O2 

Berzelius,  1826, 
Vlaanderen,  1858,  Reduct, 
Dumas,  1859,          Oxid,       2  Det. 
Van  derPlaats,  1885,  Oxid,  3  Det., 
Reduct,  4  Det., 


2  Det. 


1.27  119. 
1.272. 


Van  derPlaats,  1885,  Oxid,  3  Det.,  114—091  ;  23. 

Reduct,  4  Det.,  117—086;  31. 
Bongartz  and  Classen,  1888: 

Electr.,  ii  Det.,  Oxidat. 


Chg.   23  low. 

Mean  37  low. 
14  low. 
20  low. 
17  low. 


242  low. 


268  STRONTIUM. 


The  limit  is  almost  o.i  for  the  best  determinations. 
0.60  185,  Sn  CU  :  4  Ag,  Dumas,  1859,  R  17.    Mean    22  high. 
0.26  941,  Sn  :  Sn  Br4 : 

Bongartz  and  Classen,  1888.         "     182  high. 
0.28  851,  Sn  :  Kaa  Clo  Sn: 

Bongartz  and  Classen,  1888.         "     189  high. 
0.32  153,  Sn  :  Am 2  Cle  Sn  : 

Bongartz  and  Classen,  1888.         "     216  high. 

The  last  need  no  consideration ;  we  have  always  found 
Classen's  work  queer.  See  Bongartz  under  Sb. 

8r  =  88?  STRONTIUM. 

6  H2  O :  Sr  Clz,  6  Hz  O— 108 :  2671=0.40  449.  Chg.     15  low. 

Marignac,  1858,           6  Det.  Mean  124  high. 

Sr  O*  S  :  Sr  Cl»  =  184  :  159=1.15  723.  Chg.     10  low. 

Marignac,  1858,          3  Det.,  949  — 927;  22.  Mean  213  high. 
These  are  the  only  dry  way,  gravimetric  determinations 
available. 

Wet  Way,  silver  process,  in  short  form : 
0.73  6n  Sr  Cla  :  2  Ag,  Pelouze,  1845: 

2  Det.,  R  15.  Mean  133  low. 
Change  46  high.              Dumas,  1859: 

A  4,  Det.,    34.  "      241  low. 

B  3,  Det.,    61.  "      201  low. 

C  4,  Det.,  192.  "      156  low. 
1.14  815,  Sr  Bra  :  2  Ag,  Richards,  1894: 

1 4,  Det.,    12.  "      132  low. 

Change  46  high.           II  4,  Det.,    n.  t(      125  low. 

Ill  4,  Det.,      5.  "      121  low. 
0.65  958,  Sr  Br2  :  2  Ag  Br,  Richards,  1894: 

1 3,  Det.,      3.  "        76  low. 

Change  27  high.           II 4,  Det.,      6,  "        77  low. 

This  is  a  most  instructive  table.  We  know  the  chloride 
process  is  worse  than  the  bromide  process. 

Disregarding  the  very  variable  results  of  Dumas  on  the 
chloride,  we  may  say  that  Sr  =  87.73  according  to  Richards. 


TELLURIUM.  269 


For  Sr  as  mean  between  Ca  and  Ba,  we  should  have  88.5. 
The  only   positive   result  is  that  the  atomic  weight  of 
Strontium  remains  unknown. 


Te.  TELLURIUM. 

We  will  make  use  of  this  case  to  show  how  closely  this 
work  comes  under  the  determination  of  the  most  probable 
formula  in  ordinary  chemical  investigation. 

The  atomic  weight  of  tellurium  having  been  much  in 
doubt,  presents  a  favorable  case  for  this  parallel. 

We  shall  limit  ourselves,  as  ordinarily,  to  dry  way  pro- 
cesses with  oxygen  compounds. 

Telluric  Oxide,  Te  Oa,  and  crystallized  Telluric  Acid, 
Ho  Oo  Te  are  the  only  compounds  to  be  considered.  We 
give  the  atomic  ratios  for  Te  from  124  to  128. 

Te.  Te  :  Oxide.  Oxide  :  Acid.  Te  :  Acid. 

124  0.79  487 

125  618        0.69  163        0.55  066 

126  747  298  262 

127  874  432  458 

128  o.So  ooo  566  652 

Chg.  13  13  20 

The  change  for  o.i  is  given  to  nearest  unit  only. 
Te  :  Te  Oz,  Analytical  Determinations: 

Berzelius,  1833,               3  Det.,  057—034;     23.  Mean  0.80  042 

Wills,  1879,   I  Series,*  5  Det.,  207— 828;  379.  "                O15 

II  Series,    4  Det.,  040— 012;     28,  "              028 

Brauner,  1889,                 5  Det.,  798— 625 ;  173.  "       0.79711 

i  Det.,  by  reduction.  932 

Staudenmaier,  1895,      406^,966—935;     31.  950 

by  reduction. 

Same,  Oxide  :  Acid,     7  Det.,  553—429;   124.  0.69  440 

Same,  Te  :  Acid,           3  Det.,  518—488;     30.  0.55  508 

These  determinations,  reduced  oy  the  usual  method  of 

*  Oxidized  by  Nitric  Acid,  which  is  known  to  be  an  imperfect  agent 
or  tellurium ;  hence  great  range. 


270  TITANIUM. 


mental  arithmetic  to  atomic  weights,  using  the  change  per 
o.  i  stated,  give  the  following  very  varied  values : 

Chemist.  Te  :  Oxide.         Oxide  :  Acid.         Te  :  Acid. 

Berzelius,  128.3 

Wills,   I  128.1 

II  128.2 

Brauner,  5  I25-7 

i  127.4 

Staudenmaier,  127.4  127.05  127.25 

What  is  needed,  is  much  more  careful  work.  Brauner 
intended  to  find  low,  for  "periodic  law." 

The  "  face  of  the  returns  "  shows  that  tellurium  has  a 
higher  atomic  weight  than  iodine ;  possibly  128  is  the  value, 
and  old  Berzelius  was  right  again. 

Ti  =  48.  TITANIUM.  H.  ROSE,  1823. 

Ti  O2  :  Ti  CU=8o  :  190  =  0.42  105.  Chg.  31  high. 
H.  Rose,  1823,  5  Det.,  825  — 273;  552.  Mean  828  high. 
Demoly,  1849,  3  Det>  "  38ir  low- 

Thorpe,  1883,          6  Det.,  182— 160;     22.        "        66  high. 

Process  by  water  alone;  oxide  weighed. 
Ti  O2  :  Ti  Br4=8o  ;  368  —  0.21  739.     Change  21  high. 
Thorpe,  1885,  306^,790  —  762;  28.     Mean  36  high. 

To  Silver: 

Ti  CU  :  4  Ag=  190  :  432  =0.43  982.  Change  23  high, 
feidore  Pierre,  1847,  9  Det.,  520  —  322;  198.  Mean  450  high. 
Thorpe,  1883,  8  Det.,  015 —  978;  37.  "  17  high. 

Ti  Br4  :  4  Ag  =  368  :  432=0.85  235.  Change  23  high. 
Thorpe,  1885,  5  Det.,  241—230;  n.  Mean  50  high. 

To  Silver  Haloid : 

Ti  CU  :  4  Ag  Cl  =  190  :  574  =  0.33  101.  Chg.  18  high. 
H.  Rose,  1823.  5  Det.,  258 — 100;  158.  Mean  55  high. 
Demoly,  1849,  3  Detv  "  T48°  high- 

Thorpe,  1883,         5  Det.,  125— in  ;     14.         "  17  high. 

Ti  Br4  :  4  Ag  Br=  368  :  752  =  0.48  936.  Chg.  13  high. 
Thorpe,  1885,  4  Det.,  982  — 951 ;  31.  Mean  26  high. 

The  so-called  determinations  of  Demoly  are  a  curiosity; 


URANIUM*  271 


of  course,  Clarke  puts  them  into  his  Olla,  and  intimates  that 
it  had  no  appreciable  influence  on  the  odor  (p.  193).  Very 
natural. 

By  silver  chloride,  Rose's  55  were  brought  down  by 
Thorpe,  60  years  later,  to  17;  in  atomic  weights,  48.3  to  48.1. 
Hence,  it  seemed  proper  to  leave  the  old  hero's  name,  who 
devised  both  processes,  and  did  so  much  other  work  in  the 
spirit  of  his  teacher,  Berzelius. 

The  work  of  Thorpe  is  very  excellent,  as  it  is  for  Si.  By 
the  change  the  departure  is  easily  estimated;  generally 
above  o.i. 

Tl       204.  THALLIUM.  CROOKES,  1873. 

See  pp.  120-137  for  details  on  this  most  sensational  case 
of  atomic  weight  determinations. 

Ur       240.  URANIUM.  EBELMEN,  1842. 

O2  :  3  Ur  Oz  =  32  :  816  =  0.03  916.     Change  15  low. 
Ebelmen,  1842,  5  Det.,  949  —  867582.     Mean    3  low. 

Zimmermann,  1886,  10  Det.,  929  —  925;     4.       "         12  high. 

Here  we  have  the  contrast  between  the  "  old  "  and  the 
"  new."  Great  fear  of  lack  of  concordance,  due  to  whip  of 
"  probable  error,"  which  in  turn  is  to  give  "  high  weight " 
to  the  work  of  the  chemist. 

Then  the  oracle  (Clarke  p.  266)  will  say:  "In  short, 
"  Ebelmen's  mean  vanishes  when  combined  with  Zimmer- 
"  mann's;"  for  we  find  the  probable  error  of  the  first  0.0090, 
of  the  latter  0.0003,  or  one-thirtieth  only. 

Hence,  Zimmermann  is  30X30  =  900  times  more 
weighty  as  a  chemist,  and  one  of  his  data  counts  as  much  as 
900  of  Ebelmen!  How  simple  and  how  scientific  the  work 
of  this  oracle.  In  these  proportions  everything  goes  into 
his  olla  podrida. 

Has  any  modern  chemist  ever  protested  against  this 
horrible  treatment  meted  out  to  our  predecessors  by  that 
scientific  pasha  at  Washington?  Has  Crookes  protested, 
that  Ebelmen  is  dead? 


272  EBELMEN. 


And  now,  when  we  test  these  determinations  by  our 
standard — which  has  been  firmly  established — we  find  the 
work  of  Zimmermann  four  times  as  far  off  as  that  of 
Ebelmen,  determined  almost  half  a  century  earlier. 

Out  upon  these  "  Official— Scientists "  that  use  their 
position  in  Washington,  as  do  the  worst  politicians,  to  build 
up  a  following  in  the  American  Chemical  Society  and  to 
subdue  the  American  Association  Adv.  Sc. 

The  work  of  Wertheim,  1843,  consisted  in  igniting  the 
double  acetate  of  Ur  and  Na,  giving  Na  Uranate.  The 
starting  salt  is  too  complex;  atomic  weight  472,  entering 
twice,  or  as  944.  Resulting  Naa  O?  Ur2=638.  Atomic 
ratio  0.67  585,  change  7  high.  Results: 

Wertheim,  1843,         3  Det.,  546 — 509;  37.       Mean  62  low. 
Zimmermann,  1886,   4  Det.,  557  —  540;  17.  "    33  low. 

What  is  particularly  striking  is  the  very  low  value  7  of 
the  change  per  o.  i ;  i.  e.  in  our  language,  the  process  is 
atomically  very  dull. 

The  oxalate  method  of  Wertheim  is  still  inferior.  No 
reliable  results  can  be  obtained  by  chosing  too  complex  a 
compound  as  starting  substance,  and  working  it  towards  a 
very  blunt  ratio. 

The  recently  proposed  method  of  Armand  Gautier, 
worked  by  J.  Aloy,  has  already  been  mentioned  because  the 
author  has  withheld  the  most  essential  data  of  observation, 
and  only  stated  the  results  found  by  adopting  the  false  value 
N  =  14.04.  See  pp.  35-38. 

But  we  are  given  the  weight  of  a  cubic  centimeter  of 
nitrogen,  according  to  Lord  Rayleigh — to  the  millionth  of 
a  gramme  and  less,  by  simply  pointing  off  this  great  experi- 
menters result  per  Litre.  This  looks  very  fine,  indeed — 
"  exact  science  "  truly. 

The  method  itself  is  very  inferior,  since  the  weight  of 
nitrogen  is  multiplied  by  17  and  a  fraction;  this  magnifies 
the  errors  of  nitrogen  determination  by  seventeen ! 

Indeed,  I  doubt  if  Armand  Gautier  would  have  presented 
such  a  method  if  he  still  had  the  privilege  of  talking  over 


VANADIUM.  273 


atomic  weight  determinations  with  Schutzenberger  and 
Friedel,  as  he  was  want  to  do  when  considering  my  work. 

To  adopt  the  weight  of  nitrogen  per  unit  of  measure 
from  Lord  Rayleigh,  and  then  use  the  false  Stas  value  for 
the  atomic  weight  of  nitrogen,  disproved  by  the  same  Lord 
Rayleigh,  is  almost  too  grotesque  even  for  his  present 
associate  Moissan. 

Making  a  blunder  of  0.7  at  the  start  does  not  augur  well 
for  the  outcome.  Since  all  essential  data  of  experiment  are 
withheld,  we  cannot  tell  how  many  other  faux  pas  are  thus 
fortunately  hidden  from  our  view. 

When  Moissan  slavishly  adopts  the  false  atomic  weights 
of  the  German  Chemical  Society  we  need  expect  no  results 
worth  consideration  from  French  Chemists.  See  p.  34. 

Va  =  51.  VANADIUM.  ROSCOE.  1868. 

O2  :  Vaz  05=32  :  182^=0.17  582.         Chg.  19  low. 
Roscoe,  1868,  5  Det.,  533  —  589544.        Mean  73  low. 

This  corresponds  to  0.38  high  or  51.38.  The  experi- 
mental results  are  evidently  low,  for  some  reason. 

The  volumetric  work  given  below,  need  not  be  considered. 
What  is  wanted,  is  a  thorough  revision  of  the  dry  way  work. 

Va  O  CIV  :  3  Ag=  173.5  '  324  =  0.53  545- 
Roscoe,  1868,       A  :  6  Det.,  533  —  425;  108.     Mean  35  low. 

B  :  3  Det.,  980  —  479;  501.         "      41  high. 
Va  O  Cla  :  3  Ag  Cl  =  173.5  •  43°- 5  =0.40  302. 
Roscoe,  1868,       A  :  6  Det.,  537—  174;  362.  Mean  158  high. 
B  :  2  Det.,  391  —  333 ;     58.        "      60  high. 

Wo  =  Tu  =  184.  WOLFRAM.  SCHNEIDER,  1850. 

Wo  :  Wo  Oa  =  184  :  232  =0.79  310.  Chg.  9  high. 
Schneider,  1850,  Reduct,  5  Det., 350— 254;  96.  Mean  6  high. 

Oxidat,  3Det.,329— 324;  5.  «  17  high. 
Marchand,  1851,  Reduct,  2  Det.,  307 — 302;  5.  "  5  low. 

Oxidat,  2  Det.,  352— 321;    31.      "      26  high. 


274  WOLFRAM. 


v.  Borch,  1851,    Reduct,  7  Det.,  313 — 212;  101.  Mean  33  low. 

Oxidat,  2  Det.,  359— 339;    20.  "  39  high. 

Dumas,  1860,       Reduces  Det., 389— 259;  130.  "  2  high. 
Bernoulli,  1860,  Impure  materials. 

Persoz,  1864,        Reduct,  2Det.,324 — 304;    20.  u  4  high. 

Roscoe,  1872,       Reduct,  3  Det.,  308 — 1965112.  "  47  low. 

Oxidat,  2  Det.,  299 — 230;    69.  u  45  low. 

Waddell,  1886,    Reduct,  506^,362—311 ;    51.  "  29  high. 
Pennington  and  Smith,  1894: 

Oxidat,  9  Det.,  394— 390;      4.  "  82  high. 

Shinn,  1896,         Oxidat,  4 06^,417—377;    40.  "  81  high. 

Schneider,  1896,  Reduct,  3  Det., 323— 307;    16.  "  3  high. 

Oxidat,  3  Det., 314 — 304;    10.  "  o  high. 
Smith  and  Desi,  1894: 

Reduct,  6  Det.,  by  weighing  Ha  O  formed. 

The  last  method,  introducing  the  questionable  value  of 
hydrogen,  must  be  excluded.  Besides,  it  varies  enormously 
in  different  experiments  for  about  the  same  amount  of 
material  used.  This  series  must  be  definitely  thrown  aside. 

There  next  remains  the  other  two  series  made  by  and  for 
Professor  Smith,  giving  81  and  82  high,  or  0.9  in  atomic 
weight,  high.  It  would,  standing  by  itself,  give  185.  It  is 
claimed  that  the  material  was  specially  free  from  Molybde- 
num. 

Another  fact  is  the  extreme  accuracy  of  weighing — to  the 
thousandth  of  the  milligramme!  Where  such  a  feature  is 
prominent,  I  have  usually  found  serious  errors  in  important 
matters.  Such  spurious  accuracy  throws  doubt  on  essential 
points,  at  least  in  my  mind. 

I  have  had  no  means  of  seeing  the  unreduced  weighings. 
The  reduction  to  vacuum  is  claimed  to  have  been  made; 
ho-Wy  that  is  the  great  question.  Compare  what  happened 
in  Smith's  laboratory  with  the  reductions  of  arsenic  (see 
p.  230).  I  fear  that  systematic  errors  lurk  right  here. 

The  other  determinations  all  agree  reasonably  well. 

Oxidation  gives  uniformly  higher  results  than  reduction, 
except  in  the  case  of  Roscoe,  where  reduction  is  abnormally 
low. 


SCHNEIDER.  275 


It  may  be  best  to  summarize  all  results  as  follows,  in 
three  plainly  marked  groups: 

Reduct.  Oxidat. 

Schneider,  1850,  6  high.  17  high. 

"  1896.  3  high.  o  high. 

Marchand,  1851,  5  low.  26  high. 

Dumas,  1860,  2  high. 

Persoz,  1864,  4  high. 

Mean,  2  high.  14  high, 

v.  Borch,  1851,  33  low.  39  high. 

Roscoe,  1872,  47  low.  45  low. 

Waddell,  1886,  29  high. 

Mean,  16  low.  3  high. 

Pennington  and  Smith,  1894,  82  high. 

Shinn,  1896,  81  high. 

Mean,  81  high. 

In  the  first  group,  we  have  Ernst  Richard  Schneider  as  a 
masterly  analyst,  who  has  proved  his  Berzelian  school  in  his 
work  on  Bi  and  Sb.  Marchand  stands  equally  high.  See 
his  work  on  Hg,  S,  Ca;  he  started  Scheerer  on  Mg.  Dumas, 
in  the  dry  way,  is  a  master;  see  his  diamond  and  calcite 
work.  We  conclude  that  this  group  is  right.  For  reduc- 
tion, this  mean  gives  184.02;  for  oxidation,  184.15,  which  is 
throughout  the  less  reliable. 

Concerning  the  second  group,  we  have  no  evidence  that 
Roscoe  did  the  work;  probably  two  chemical  students,  called 
"analyst  A"  and  aB  "  did  the  work.  The  other  two  ana- 
lysts are  not  known  by  any  other  work  of  this  kind,  good  or 
bad.  Hence,  this  group  possesses  no  weight. 

There  remains  the  third  group,  comprising  oxidation 
work  done  by  or  under  Prof.  Smith. 

We  have  already  stated  why  we  cannot  accept  his  record 
in  this  case.  The  process  by  weighing  the  water  was  decid- 
edly imperfect  in  execution — the  curve  of  errors  running 
straight  up.  We  have  on  record  bad  breaks  in  reduction  to 
vacuum  (see  pp.  229-231)  and  from  the  formula  used  (see 
p.  175)  need  not  wonder  thereat.  The  excessive  accuracy  in 
weighing  {fancied,  and  drilled  into  that  institution  through 
Professor  Barker)  must  detract  from  essentials. 


276  ZINC. 

When  Professor  E.  F.  Smith,  in  1899,  (Journal  American 
Chemical  Society,  1899,  p.  1022),  concludes,  "  it  is  evident 
"  that  no  reliable  atomic  mass  determinations  can  be  made 
u  by  the  oxidation  of  metallic  tungsten  "  we  may  agree,  if 
he  means  the  atomic  "weight,  we  have  really  used  reduction 
results,  only. 

But  his  reason  stated  looks  very  insufficient;  (1.  c.,  p. 
1022).  We  need  only  put  it  into  plain  form,  in  milli- 
grammes. We  find  a  loss  of  i.o  per  process,  a  round — and 
it  is  no  doubt  due  to  the  oxidation  part  of  the  round. 

For  these — and  other  reasons — we  must  decline  to  con- 
sider the  work  of  Smith  and  his  students  of  any  value  in 
comparison  to  the  work  summarized  in  our  first  group,  done 
by  known  and  proved  masters. 

There  is  one  other  reason,  which  I  have  not  stated,  and 
which  others  cannot  as  fully  appreciate  as  I  have  learned  to 
do.  It  is  the  high  praise  from  Clarke,  see  page  259 
(extremely  low  probable  error) ;  p.  260.  (P.  and  S.  vastly 
outweighs  everything  else) ;  p.  263  (work  in  Smith's  labora- 
tory dominates  all  the  rest). 

Knowing,  by  long  experience,  that  Clarke's  opinion, 
being  based  on  a  false  formalism,  is  not  only  worthless,  but 
invariably  on  the  side  of  error,  I  see  this,  my  opinion, 
most  strikingly  verified  in  this  instance. 

If  there  is  a  case  in  which  this  author  of  weighing  and 
judging  chemical  work  is  right  (Clarke),  I  should  be 
delighted  to  have  it  pointed  out  to  me. 

Zn  =  65.  ZINC.         AXEL  ERDMANN,  1844. 

Zn  :  Zn  Orrr  65  :  81  =0.80  247.     Change  24  high. 
Jacquelin,  1842: 

Wet  way,  4  Det.,  570  —  524;  46.     Mean  296  high. 
Axel  Erdmann,  1844; 

Dry  way,  4  Det,  274  —  247;  27.        "         13  high. 
Morse  and  Burton,  1888: 

15  Det.,  320  — 305;  15.         u        65  high. 
Recent  work  on  absorption  of  oxygen  by  the  oxide,  has 
not  been  sufficiently  studied,  not  having  had  access  to  the 
details. 


AXEL     ERDMANN.  277 


The  work  of  Axel  Erdmann  was  undertaken  at  the 
request  of  Berzelius,  and  reported  by  him  to  the  Swedish 
Academy,  and  in  his  Annual  Report,  March  31,  1844, 
(French  Series,  transl.  Plantamour,  No.  5,  p.  71;  Paris, 
1845).  He  found  it  necessary  to  use  porcelain  crucibles. 

The  entire  range  is  only  equivalent  to  o.i  on  the  atomic 
weight,  while  the  analytical  excess  of  the  mean  represents 
only  0.05  high.  Crucible  work  in  those  days  was  quite  dif- 
ferent from  what  it  is  now. 

From  all  I  can  tell,  by  looking  carefully  over  the  entire 
mass  of  work  done,  I  must  conclude  this  to  be  the  true 
value. 

The  determinations  made  since  1844  have  been  very 
numerous,  especially  in  more  recent  years. 

We  have  even  a  goodly  number  of  determinations  by 
students,  called  "  practice  work  of  students;"  but  such  work 
should  remain  sacred  to  the  laboratory,  and  not  be  published 
as  atomic  weight  determinations  (under  Morse  and  Keiser, 
in  Johns  Hopkins  University,  Baltimore,  containing  51 
determinations;  see  Clarke,  p.  150,  who  puts  the  mean  in 
his  Olla  Podrida,  of  course). 

All  determinations  by  means  of  hydrogen  must,  at  pres- 
ent, be  ruled  out,  because  of  the  uncertainty  affecting  the 
latter.  This  excludes  Van  der  Plaats,  1887,  Mallet,  1890;  and 
the  student's  work. 

Of  the  wet  way  processes,  we  must  note  the  most  preten- 
tious by  Richards  and  Rogers,  of  Harvard  University,  which 
point  to  65.5  as  the  atomic  weight  of  Zinc.  We  calculate  for 
this  value  65.5: 

Zn  Br2  :  2  Ag— 225.5  :  216=1.04  398.     Chg.  46  high. 
Series  A  No  Ag  determination. 

"      B  4  Det.,  411  —  376535.  Mean    6  low. 

"      C  3  Det.,  380  — 377;     3.  "       19  low. 

Zn  Br2  :  2  Ag  Br=225-5  :  376  =  0.59  973.  Chg.  26  high. 
Series  A  5  Det.,  984  —  961;  23.  Mean     2  high. 

"     B  4  Det.,  977  — 959;  18.  "        6  low. 

"     D  3  Det.,  962  —  961 ;     i.  "       12  low. 

Richards  sacrifices  everything  to  concordance,  as  well 
known,  and  specially  striking  in  the  present  work.  In  the 


278  REDUCTION    TO    AIR. 

silver  process,  he  reduces  the  range  to  one-tenth,  but 
increases  the  analytical  excess  threefold.  In  the  silver  bro- 
mide process,  he  reduces  the  range  from  23  to  i,  while  the 
analytical  excess  is  lowered  from  2  high  to  12  low! 

I  must  confess  that  I  have,  for  some  time,  thought  this 
work  reasonably  reliable,  on  account  of  its  being  done  with 
bromine,  and  not  with  chlorine. 

But  upon  carefully  looking  over  the  entire  field,  and 
remembering  the  ordinary  deviation  of  this  wet  way  work 
(which  for  the  most  concordant  brings  it  0.05  below)  I  am 
compelled  to  drop  this  as  fictitious,  and  to  adopt  the  dry 
way  work  of  Axel  Erdmann  done  under  the  old  master's 
eye,  before  modern  fancy  methods  got  a  start. 

Indeed,  the  record  of  the  determination  of  the  atomic 
weight  of  zinc,  since  1850,  is  a  disgraceful  one;  even  Mar- 
ignac,  in  1883,  went  astray. 

It  is  to  be  hoped,  that  strictly  rational,  common  sense 
work  of  revision  will  be  done  for  this  metal  at  an  early  day. 

Zr  =  90.  ZIRCONIUM. 

ZrOz  :  Zr  (Ch  8)2  —  122  :  282—0.43  262.  Chg.  21  high. 
Berzelius,  1825,  6  Det.,  Mean  128  low. 

Weibull,  1881,          7  Det.,  321  — 081 ;  241.         "       112  low. 
Bailey,  1889,  8  Det.,  402  —  337;     65.         "       no  low. 

ZrO2  :  Zr  (O4  Se)2  — 122  1376  =  0.32  447.  Chg.  18  high. 
Bailey,  1889,  5  Det.,  640  —  470;  170.  Mean  in  high. 

It  is  apparent  that  the  results  from  the  selenate  would 
raise  the  atomic  weight  as  much  as  those  from  the  sulphate 
would  lower  it,  namely,  0.5.  We,  therefore,  leave  it  at  90. 

ADDENDA  TO  PART  SECOND. 

I.     REDUCTION  TO  AIR. 

The  Reduction  to  Vacuum  was  condemned  by  Berzelius. 
H-e  considered  it  a  mere  "gnat"  in  comparison  to  the 
unavoidable  errors  of  all  other  operations  involved. 

We  have  found  this  opinion  of  Berzelius  to  be  exactly  true. 

Besides,  we  have  shown  that  this  pretended  "  correction  " 


REDUCTION    TO    AIR.  279 


of  the  experimental  determinations  de  facto  introduces 
gross  errors  in  practice. 

We  will  here  only  refer  to  the  errors  of  12  and  66  milli- 
grammes "  inadvertantly  "  committed  by  Stas  in  Nos.  8  and 
6  of  his  famous  syntheses  of  silver  nitrate.  See  pp.  175-176. 

We  may  also  recall  the  remarkable  "  rise  "  in  Nos.  5  and 
8  of  the  determinations  of  arsenic,  though  the  reduction  of 
necessity  involves  a  lowering  of  the  ratio.  See  p.  230. 

By  a  most  astonishing  play  of  fate,  in  all  these  cases  of 
"inadvertency"  the  result  was  a  "smoothening  of  the 
curve,"  a  most  notable  diminution  of  the  deviations  from  a 
constant  mean,  a  truly  wonderful  diminution  of  residual 
"errors." 

How  strange  that  such  inadvertent  errors  should  reduce 
the  actual  errors  so  as  to  reduce  the  final  probable  error  of 
the  mean! 

We  have  strongly  advised  to  leave  the  weighings  without 
reducing  them  to  vacuum. 

We  must  insist  on  giving  the  actual  weighings  in  air  in  all 
cases,  even  if  the  weighings  reduced  to  vacuum  are  given  also. 

The  former  are  the  true  results  of  observation ;  the  latter 
\ve  have  seen  to  be  often  affected  with  very  large  errors,  due 
to  errors  of  calculation— or  other  causes. 

I  shall  here  show  how  superfluous  this  entire  reduction  to 
vacuum  is,  and  how  the  exact  comparison  can  be  made  by 
the  following  most  simple  process  of  calculation. 

This  process  consists  in  calculating  the  change  of  our 
absolute  atomic  ratio  due  to  the  buoyancy  of  the  air. 

In  other  words,  we  prefer  to  reduce  our  absolute  weights 
to  air,  the  very  opposite  of  the  common  process. 

By  the  well  known  method,  reduction  to  vacuum  there  is 
a  certain  small  factor  k  milligramme  per  gramme  to  be 
added  to  the  apparent  weight  or  the  weight  in  air. 

Consequently,  the  apparent  weight  will  be  obtained  from 
the  absolute  weight,  by  subtracting  this  small  amount. 

These  factors  have  been  tabulated  by  Kohlrausch  (Leit- 
faden,  IV  Aufl.,  1880,  p.  286;  also  Ostwald,  Hand  und 
Hilfsbuch,  1893;  p.  47;  also  my  General  Chemistry,  1897, 
pp.  220  and  231). 


28O  REDUCTION    TO    AIR. 

For  a  quotient,  the  minute  correction  is  obtained  by 
subtracting  the  correction  of  the  divisor  from  that  of  the 
dividend,  as  is  well  known. 

Let  us  apply  this  process  to  the  case  of  arsenic. 

The  dividend  is  234,  the  absolute  weight  of  the  salt, 
formed  from  354  of  pyroarsenate,  the  divisor. 

The  specific  gravity  of  salt  is  2.16,  which  gives  its  factor 
0.41  milligrammes  per  gramme,  allowing  for  brass  weights. 

The  specific  gravity  of  the  pyroarsenate  was  (by  Hibbs) 
taken  at  2.295  ^or  which  we  take  2.30;  this  gives  the  factor 
0.38  milligrammes  per  gramme. 

Reducing  to  air,  makes  the  sign  opposite;  hence  result- 
ing factor  for  the  fraction  is 

—  0.41  —  ( —  0.38)  which  is  —  0.03, 

that  is  a  subtraction  of  0.03  milligrammes  per  gramme,  or 
3  units  in  the  fifth  place. 

But  the  ratio  is  0.66  102  for  which  we  take  here  0.66, 
that  is  %. 

Now  %  times  3  is  2 ;  the  sign  being  negative,  we  see  that 
in  this  case 

the   reduction    of  our    absolute   atomic    ratio  to   air  is 
obtained  by  adding  tivo  units  in  the  fifth  decimal. 

If  now,  we  wish  to  reduce  the  actual  weighings  given 
p.  207  to  vacuum,  we  simply  need  to  subtract  two  units  in 
the  fifth  place. 

The  table,  p.  230,  will  now  show  how  remarkable  are  the 
errors  of  reduction  actually  committed. 

Of  course,  we  must  retain  our  absolute  atomic  ratios 
pure  and  simple,  and  merely  calculate  this  reduction  to  air 
in  the  manner  shown  to  be  able  to  allow  for  actual 
differences  observed. 

As  the  slight  variations  produced  by  changing  tempera- 
ture and  pressure  fix  only  the  correction  of  a  correction, 
that  is,  a  minute  quantity  of  second  order,  they  are  usually 
entirely  insignificant.  Sufficient  data  for  the  allowance  are 
given  in  my  General  Chemistry,  231,  note. 

To  complete  this  subject,  we  state  how  the  minute  factor 
referred  to  above  is  actually  obtained. 


CROOKES'    DECIMALS.  28l 

The  weight  of  one  cubic  centimeter  of  air,  at  common 
temperatures  and  pressures,  is  1.2  milligrammes. 

If  S  is  the  specific  gravity  (i.  e.,  grammes  per  cc),  then 
the  specific  volume  is  i  divided  by  S  (cc  per  gramme). 

Hence  the  weight  of  one  gramme  of  this  substance  is 
buoyed  up  by  1.2/8  milligrammes. 

The  brass  -weights  (spec.  grav.  8.5)  are,  therefore,  buoyed 
up  by  0.14  milligrammes  per  gramme.  As  they  are  on  the 
opposite  pan,  it  must  be  subtracted  from  the  buoyancy  of 
the  substance  weighed. 

For  Salt,  S  =  2.16  gives  1.2/8  =  0.55;  corrected  for  brass 
weights  0.55  —  o.  14  =  0.41 . 

For  Pyroarsenate  S:=  2.30  gives  1.2/8=0.52;  corrected 
for  brass  weights,  0.38. 

These  are  the  minute  factors  above  used. 

In  this  way,  a  most  simple  calculation  will  quickly  show, 
how  many  units  in  the  fifth  place  the  absolute  atomic  ratio 
will  be  lowered  or  raised  by  the  buoyancy  of  the  air. 

No  calculations  are  to  be  made  for  each  individual 
determination;  only  one  single  and  most  simple  calculation 
for  the  entire  process.  See  pp.  64-65. 

If  this  direction  is  followed  to  the  letter,  there  will  not 
be  any  chance  for  such  deplorable  inadvertent  mistakes  in 
the  reduction  to  vacuum  as  have  disfigured  the  work  of 
Stas  and  his  disciples — until  we  lifted  the  veil  of  mystery 
and  fraudulent  exactitude  that  has  hid  them  for  so  many 
years. 


II.     HOW  CROOKES  MANUFACTURED  DECIMALS. 

In  the  absence  of  the  Philosophical  Transactions  (see  p. 
122),  I  supposed  that  the  last  three  decimals  had  been 
"  determined "  by  Grookes  by  the  oscillation  method 
(p.  129). 

Looking  at  a  book  in  the  hands  of  my  son,  taken  by  him 
from  the  Mercantile  Library,  I  find  it  to  be  Crookes'  Select 
Methods  in  Chemical  Analysis,  II  edition,  London,  1886. 


282  HOW    CROOKES 


Opening  this  volume,  I  see  near  its  close  pages  with 
many  decimals  (pp.  687-691)  which  naturally  attract  my 
attention. 

I  discover  with  joy  a  part  of  Crookes'  Memoir  on  the 
atomic  weight  of  thallium,  reprinted  from  the  Philosophical 
Transactions  of  1873. 

In  a  few  minutes  I  learn  how  Crookes  actually  obtained 
his  wonderful  weighings  to  the  millionth  of  the  grain,  by 
reading  kotv  he  obtained  the  more  wonderful  weighings  to  the 
thousand-millionth  of  a  grain* 

Das  geht  denn  doch  iiber  das  Bohnenlied! 

Crookes  did  not  tamper  with  the  individual  weighing* ; 
he  falsified  his  weights. 

The  Modus  Operand!. 

Mr.  William  Crookes,  in  the  summer  of  1864,  adjusted 
and  tested  an  evidently  fine  set  of  platinum  grain  weights 
(1.  c.,  p.  686). 

The  testing  was  done  according  to  the  ordinary  method, 
taking  the  largest  weight  as  standard  of  comparison.  This 
is  a  thousand  grain  weight  (about  65  grammes). 

Since  1864  he  has  repeatedly  tested  these  weights;  "  they 
have  shown  up  to  the  present  time,  absolutely  no  alteration  " 
(p.  691). 

"  The  present  time,"  is  1873,  when  that  paper  was 
printed  in  the  Philosophical  Transactions. 

Since  it  is  reprinted  by  Mr.  William  Crookes,  in  1886, 
without  dissent  or  annotation,  we  are  entitled  to  conclude 
that  his  set  of  platinum  weights  had  shown  "  absolutely  no 
alteration"  even  to  1886,  that  is  in  22  years. 

It  is  surely  a  most  excellent  set  of  weights,  and  Mr. 
Crookes  has  handled  it  most  carefully. 

On  page  688  we  find  an  important  item  about  the  balance, 
apparently  the  very  one  "  specially  constructed  for  that 
research."  (see  p.  122,  supra).  I  must  quote  this  footnote, 
for  I  want  to  be  fair,  always;  the  italics  are  ours. 

"  Although  these  decimals  are  carried  to  the  sixth  place, 
li  the  balance  would  not  indicate  beyond  the  fourth  place.  By 
"  taking  the  mean  of  ten  interchanged  weighings,  I  could 


MAKES     DECIMALS.  283 

"  obtain  a  fifth  place.  The  calculated  values  of  the  weights 
"  were  carried  to  the  sixth  decimal,  in  order  to  avoid  inac- 
l<  curacy  in  the  fourth  and  fifth  places  when  several  values 
"  were  summed.'* 

If  Mr.  William  Crookes  had  strictly  carried  out  this 
intention,  and  in  the  published  results  dropped  the  last  two 
places,  he  would  have  only  subjected  himself  to  needless 
drudgery. 

But  on  page  691  he  gives  a  table  of  the  individual  weights 
of  his  fine  set  to  the  sixth  place,  that  is  to  the  millionth  of  a 
grain;  and  there  can  remain  no  doubt  but  by  this  table  he 
summed  up  his  actual  weighings,  and  obtained  the  millionth 
of  the  grain  in  his  published  results,  requiring  "  expurga- 
tion "  at  our  hands,  see  p.  128,  supra. 

The/a^  that  "  Crookes  continued  calculating  till  he  got 
tired,  and  did  not  get  tired  till  he  had  passed  the  limit  of 
precision  by  three  places  beyond  the  ken  of  his  balance,"  as 
we  surmised  (pp.  129-130,  supra)  remains. 

According  to  his  own  footnote  he  passed  it  by  t-wo  places. 

Instead  of  using  the  oscillation  method,  he  simply  used 
his  actual  weights  to  the  hundredth  of  a  grain  (%  rngr.)  and 
a  rider  of  this  weight. 

All  the  decimals  beyond  this — and  there  are  four  of  them 
— are  the  result  of  his  weighing  of  his  weights,  the  compari- 
son of  his  actual  set  of  platinum  weights,  by  means  of  his 
balance  "that  would  not  indicate  beyond  the  fourth  place." 

He  has  also  adjusted  a  rider  of  o.oi  grains,  which  would 
give  him  the  fourth  decimal,  which  his  balance  will  "indi- 
cate," but  not  determine. 

How  very  readily  Mr.  William  Crookes  takes  decimals  is 
shown  in  a  striking  manner  in  the  extract  from  his  paper 
in  question,  reprinted  in  his  "Select  Methods"  of  1886, 
before  me. 

The  loco  grain  weight  he  balances  by  the  600-1-300-]-  100 
and  o.oi  grain;  that  is  solid  work,  to  the  hundredth  of  a 
grain  (=%mgr.). 

His  600  grain  weight  is  determined  to  five  places,  as  are 
all  other  weights;  that  is,  the  balance  responds  only  to  the 
fourth,  but  10  trials  give  him  a  mean  to  the  fifth. 


284  CROOKES'     DECIMALS. 

According  to  Crookes,  there  are  no  constant  errors;  the 
mean  is  right.  See  p.  46,  supra. 

In  his  calculations  he  does  not  tire  (see  p.  130,  supra). 
Up  to  Equation  E  he  gives  5  decimals;  but  from  F  he 
already  gets  6,  from  K  he  gets  7,  from  P  he  gets  8,  from 
U  he  gets  9  and  keeps  getting  9  decimals  till  the  last  Equa- 
tion, Z. 

Thus,  the  "  exact  weight "  of  his  rider  is  given  (1.  c., 
p.  690.)  0.009  996  997  grain. 

To  use  this  figure  instead  of  o.oio  is  the  manifestation  of 
the  most  colossal  stupidity;  for  it  asserts  the  actual  tangible 
determination  of  o.ooo  003  003  grains  by  means  of  a  bal- 
ance giving  only  o.ooi  with  certainty. 

To  give  the  weight  of  a  platinum  wire  to  the  thousand- 
millionth  by  weighing  it  to  the  thousandth  on  a  balance 
barely  sensitive  to  the  ten  thousandth,  is  a  feat  to  which 
nothing  in  modern  science  is  comparable. 

We  have  to  go  back  to  the  days  of  Isaac  Abensid  (Hassan), 
under  Alphons,  King  of  Castile,  some  seven  centuries  ago 
to  match  it,  when  the  daily  motion  of  the  moon  was  given 
to  8  sexagesimal  places.  Madler,  Geschichte,  I,  p.  101 ;  1873. 

In  this  manner,  by  numerical  elimination,  grinding  out 
with  pencil  on  paper  from  5  to  9  decimals  of  the  grain, 
Crookes  weighed  to  the  ninth  decimal  of  the  grain  on  his 
balance! 

We  must  be  profoundly  thankful,  that  Mr.  William 
Crookes  did  not  work  in  all  of  his  9  decimals,  but  in  his 
table  chopped  off  the  last  three. 

In  this  way  he  "weighed  his  weights"  to  the  millionth 
of  the  grain. 

He  "  summed  "  this  value  of  his  weights  on  the  pan — 
and,  of  course,  obtained  the  weight  of  his  thallium  and  its 
nitrate  to  the  millionth  of  the  grain! 

And  I  had  supposed  that  Mr.  William  Crookes  "  deter- 
mined each  weighing  independently,  by  the  oscillation 
method! 

But  the  fraud  and  the  imposition  remain  the  same — only 
a  little  more  so,  because  of  the  greater  clumsiness  of  the 
process. 


DEGREE    OF    CERTAINTY.  285 


CONCLUDING    REMARKS. 


I.     THE  DEGREE  OF  CERTAINTY  ATTAINED. 

Having  completed  the  exposition  of  the  actual  analytical 
determinations  made  during  the  century  just  closed,  and 
having  also  given  a  final  reductio  ad  absurdum  of  the  system 
of  Stas,  pp.  169-209,  we  must  close  the  entire  work  with  a 
numerical  summary  of  the  evidence  of  the  exact  commen- 
surability  of  the  true  atomic  weights  of  the  chemical  elements 
and  of  the  unity  of  matter. 

The  manner  of  procedure  in  this  demonstration  has  been 
fully  explained  on  pp.  212-214.  We  may  repeat  the  method 
here  in  more  general  terms.  . 

If  the  measure  of  precision  of  the  true  atomic  weight  be 
p  which  is  the  n*h  part  of  a  unit,  then  the  certainty  is  as  n 
to  i  for  one,  »2  to  i  for  2,  »>»  to  i  for  m  elements  all  termi- 
nating their  true  atomic  weight  with  the  full  natural  number. 

Is  p  =  0.001  then  »zr:iooo;  for  5  such  elements,  «5  is 
one  followed  by  5 -x  3  =115  ciphers. 

\Ve  shall  now  enumerate  the  elements  in  groups  accord- 
ing to  this  degree  of  precision. 

I.  For  the  following  eleven  elements  the  precision  of 
determination  of  this  absolute  atomic  weight  reaches  o.ooi ; 
hence,  one  thousand  divisions  of  the  unit  giving  for  all  the 
termination  .000,  represents  one  chance  in  1000  raised  to  the 
eleventh  power,  which  is  expressed  by  the  number  one  fol- 
lowed by  33  ciphers. 

The  eleven  elements  here  referred  to  are :  Ag,  As,  Bo, 
Br,  C,  Cd,  Cu,  N,  O,  P,  Tl. 

We  could  also  say,  that  this  number 

IOOO  OOOOOO  OOOOOO  OOOOOO  OOOOOO  OOOOOO 

compared  to  one  represents  the  certainty  that  these  eleven 
elements  are  composed  of  but  one  primitive  material,  the 
atomic  weight  of  which  is  one  twenty-fourth  of  that  of  car- 
bon-diamond. We  have  called  this  primitive  material 

PAXTOGEN. 

II.  For  the   three   elements,    Fl,    H,  Li,  the   precision 
does  not  exceed  0.002,  of  which  500  make  one  unit.     Hence, 


286  PRECISION 

the    corresponding  factor   of  certainty  is  500  in  the  third 
power,  which  is  125  oooooo. 

III.  For  the  two  elements,  lo  and  Mo,  the  precision  is 
only  0.005,  of  which  200  make   one  unit.     Hence,  the  cor- 
responding factor  of  certainty  is  200  in  the  second  power, 
or  40  ooo. 

IV.  For  the  following  nine  elements  Ca,  Cl,  Fe,  Hg, 
Mg,  Na,  Pb,  Pt,  S,  the  precision  attained  is  o.oi  of  which 
loo  go  to  a  unit.     The  corresponding  factor  of  certainty  is, 
therefore,  100  raised  to  the  ninth  power,  that  is 

i  oooooo  oooooo  oooooo, 
or  one  followed  by  18  ciphers. 

The  certainty  of  the  entire  result  is  the  product  of  these 
factors,  tabulated  below.  The  single  factors  are  resolved  in 
the  numerical  part  and  the  number  of  ciphers  following,  so 
that  the  final  product  can  be  most  readily  determined. 

We  also  once  more  enumerate  the  actual  individual 
elements  of  each  group. 

Group.     Precision.     No.                Elements.                          Factor.  Ciphers. 
I          o.ooi       ii     Ag,  As,  Bo,  Br,  C,  Cd, 

Cu,  N,  O,  P,  Tl,                  i  33 

II          0.002        3     Fl,  H,  Li,                             125  6 

III  0.005         2     I°>  M°>                                      4  4 

IV  o.oi          9     Ca,  Cl,  Fe,  Hg,  Mg,  Na, 

Pb,  Pt,  S,  i  18 

Total :     25     Elements,  500  61 

or  5000  followed  by  60  ciphers, 

or  5000  followed  by  10  times  the  million  group  of  6 
ciphers. 

This  number  is  exactly  five  thousand  times  the  greatest 
number  ever  formulated  by  antiquity,  namely,  by  Archi- 
medes of  Syracuse,  in  his  Arenary  or  Sand-Calculus.  He 
obtained  (in  our  notation)  the  number  i  followed  by  sixty 
ciphers,  by  estimating  the  number  of  grains  of  sand  that 
could  be  contained  in  the  entire  universe  as  then  known. 
See  the  admirable  French  translation  of  his  works,  by  F. 
Peyraud,  Tome  II,  p.  231-264;  Paris,  1808. 


AND    CERTAINTY.  287 


We  may  consider  this  number  practically  infinite,  under 
all  ordinary  human  conditions.^ 

Hence,  we  can  say,  that  the  twenty-five  chemical  ele- 
ments enumerated,  for  which  the  true  atomic  weight  is 
known  with  a  degree  of  precision  of  at  least  o.oi  of  a  unit, 
are  hereby  proved  to  be  compounds  of  one  single  material, 
the  atomic  weight  of  which  is  one-half  a  unit,  or  •£$  of  our 
standard  of  matter,  the  diamond-carbon. 

The  chance  that  this  conclusion  is  an  error  is  as  one  is 
to  the  practically  infinite  number  just  given,  namely,  5000 
followed  by  ten  times  the  million  group  of  six  ciphers. 

We  can  also  state  the  same  conclusion  by  saying  its  cer- 
tainty is  expressed  by  this  same  number,  the  chance  of  an 
error  being  unity. 

Since  now  these  twenty-five  chemical  elements  were  not 
chosen  or  selected  by  us  for  any  special  reason  other  than 
the  accuracy  or  the  degree  of  precision  wherewith  their 
atomic  weight  has  been  determined,  this  conclusion  applies 
to  any  and  every  group  of  25  chemical  elements,  that  is,  to 
all  chemical  elements,  even  those  not  yet  known  to  us. 

These  25  elements  comprise  fully  one-third  of  all  ele- 
ments known  to-day.  They  include  nearly  all  the  best 
known  and  most  important  of  these  chemical  elements. 

As  soon  as  the  atomic  weight  determinations  shall  be 
carried  on  in  a  rational  manner,  in  accordance  with  the 
principles  laid  down  in  this  work  and  in  our  True  Atomic 
Weights  of  1894,  the  required  precision  will  be  obtained  and 
the  elements  will  fall  into  line. 

It  is  easily  determined  that  the  certainty  for  all  38  ele- 
ments now  determined  with  a  precision  of  o.i  or  more  is 

800  followed  by  thirteen  times  the  million-group  of 

6  ciphers, 

which  is  800  oooooo  oooooo  oooooo 

times  the  greatest  number  of  antiquity  of  Archimedes. 

The  thirteen  additional  elements  here  referred  to  are: 

V    Al,  Bi,  Ur,  precision  0.02 ; 
VI     Au,  Be,  In,  Mn,  Se,  Wo,  Zn,  precfsion  0.05; 
VII     Sb,  Sn,  Ti,  precision  o.i. 


288  FIND    ONE   NEEDLE    IN 

II.     THAT  STELLAR  HAYSTACK. 

Since  we  have  shown  (p.  213)  that  for  the  12  elements  the 
certainty  was  I  followed  by  four  times  the  million  group  of 
six  cyphers,  it  follows  that 

the  certainty  of  38  elements  is  800  followed  by  nine 
times  the  million  group  of  six  ciphers 
times  as  great 

as  for  the  12  elements  referred  to. 

Since  the  solitary  needle  in  the  haystack  covering  a  globe 
a  thousand  times  the  radius  of  our  earth,  was  found  to 
represent  the  one  chance  that  we  are  wrong  in  our  conclu- 
sion, based  upon  the  determinations  of  twelve  elements,  we 
must  try  to  find  the  base  of  the  haystack  corresponding  to 
the  chance  of  error  for  the  38  elements  here  considered. 

Since  the  square  root  of  800  is  a  little  over  28,  it  follows 
that  the  square  root  of  the  last  number  given  Is 

28  ooo  followed  by  four  times  the  million  group  of  six 
ciphers. 

Accordingly,  the  radius  of  the  globe  having  the  neces- 
sary surface  to  hold  the  haystack  for  the  38  elements  is  this 
number  of  times  the  thousand  radii  of  the  earth  which 
formed  the  base  for  the  haystack  for  the  dozen  elements; 
p.  217. 

In  other  words,  the  radius  of  the  globe  having  the  neces- 
sary surface  to  hold  our  38  element  haystack  is 

28  followed  by  five  times  the  million  group  of  six  ciphers 

times  the  radius  of  our  earth. 

The  sun's  distance  from  the  earth  is  23  150  times  the 
radius  of  the  earth. 

Dividing  this  into  the  above,  we  get  (enlarging  the 
divisor  to  28  ooo  for  convenience  of  division,  and  to 
strengthen  our  result)  : 

The  globe  having  a  surface  equal  to  the  haystack  for 
38  elements  must  have  a  radius  over  1000  followed 
by  four  times  the  million  group  of  six  ciphers  times 
the  earth's  distance  from  the  sun. 

Since  the  distance  from  the  sun  to  Neptune,  the  most 
distant  planet  known,  is  only  30  times  as  great  as  the  dis- 


THAT   STELLAR   HAYSTACK. 


tance  from  the  sun  to  the  earth,  the  radius  required  passes 
far  beyond  our  planetary  system  into  stellar  space. 

The  researches  on  the  parallax  of  the  stars  have  shown, 
that  stars  like  61  Cygni  and  a  Centauri  are  distant  less  than 
half  a  million  times  the  distance  from  the  earth  to  the  sun. 

At  a  million  times  the  distance  —  earth-sun  —  we,  there- 
fore, are  beyond  the  distance  for  which  it  has  been  possible 
to  estimate  stellar  distances  by  the  most  refined  astronomical 
researches. 

But  the  radius  of  the  globe  to  hold  our  38  element  hay- 
stack must  be 

I  000  000000  000000  000000 

times  as  large  as  this  distance  of  the  ordinary  stars! 

From  such  a  distance  no  light  has  ever  reached  human 
eye,  even  by  means  of  the  great  speculum,  six  feet  in 
diameter,  of  the  Earl  of  Rosse  at  Parsonstown,  Ireland. 

We  give  it  up.  We  cannot  convey  any  tangible  concep- 
tion of  the  number  presented.  It  is  infinite  for  the  mind  of 
finite  man. 

But  if  the  haystack  has  a  base  inconceivably  larger  than 
the  stellar  world  visible  to  us,  and  if  the  chance  of  our 
conclusion  being  in  error  is  no  greater  than  that  of  finding 
a  single  needle  in  this  infinite  haystack,  may  we  not  say  that 
our  conclusion  is  proved  true  with  greater  certainty  than 
any  other  scientific  conclusion  ever  drawn  about  nature! 

We,  therefore,  are  entitled  to  state  this  conclusion  once 
more  in  words  (see  pp.  217  and  218)  : 

The  atomic  weight  of    all    chemical    elements    are 
exactly  commensurable; 

the  greatest  common  divisor  of  all  is  half  a  unit, 
the  atomic  weight  of  carbon-diamond  being  taken  at 
12  exactly; 

therefore,  the  atoms  of  the  chemical  elements  are 
composed  of  but  one  kind  of  primitive  atoms,  of 
pantogen,  the  atomic  weight  of  which  is  exactly  half 
our  unit;  and 

the  great  majority  of  element-atoms  consist  of  an 
even  number  of  such  pan-atoms. 


290  ATOMIC     NUMBERS. 


III.    TABLE  OF  ATOMIC  NUMBERS. 

Hence  also  the  number  of  atoms  of  pantogen  contained  in 
one  atom  of  any  given  element,  is  exactly  two  times  the  true 
atomic  weight  of  that  element,  the  atomic  weight  of  carbon- 
diamond  being  taken  at  12  exactly. 

This  number  we  call  the  atomic  number  (Atomzahl  in 
German);  we  have  also  called  it  atogramme  in  our  Pro- 
gramme of  1867.  Compare  pp.  217-218,  supra. 

While  this  is  not  the  place  for  the  study  of  this  most 
important  subject,  which  we  shall  take  up  in  "another  work, 
we  deem  it  sufficiently  interesting  to  give  a  table  of  atomic 
numbers  for  the  most  important  chemical  elements. 

The  arrangement  and  order  of  the  elements,  we  take 
from  Part  III,  pp.  205-256,  of  our  True  Atomic  Weights, 
1894,  and  from  pp.  200-201  of  our  Introduction  to  General 
Chemistry,  1897. 

Table  of  Atomic  Numbers. 

I.     THE  CARBON  SYSTEM;  from  Positive  to  Negative. 


Valence 

fe 

"5 
,0 

s*, 

cc 

a 

£ 

T3 

c 

0 

o 
u 

C/3 

•g 

in 
P 

j~ 

£ 

fe 

M 

£ 

I 

Kaloids, 

Ka 

Li 

H 

Na 

46 

2 

Cadmoids, 

Kd 

Be 

18 

Mg 

48 

Zn 

130 

Cd 

224 

Hg4oo 

3 

Styptoids, 

IT 

Bo 

22 

Al 

54 



— 

Tl   408 

4 

Adamantoids, 

Ad 

C 

24 

Si 

56 



Sn 

236 

Pb4i4 

3 

Phosphoids, 

0 

N 

28 

P 

62 

As 

J50 

Sb 

240 

Bi   416 

2 

Sulphoids, 

8 

0 

32 

S 

64 

Se 

153 

Te 



I 

Chloroids, 

X 

Fl 

38 

Cl 

7i 

Br 

160 

lo 

254 



Lighter,  Earthy— Metals : 

1  Kaloids,  Ka  Ka  78        Rb Cs  266 

2  Calcoids,  Xa  Ca  80        Sr  -        Ba  274 

II.     THE  IRON-SYSTEM;  from  Negative  to  Positive. 

Va    102 
Molybdoids,  MX  Cr    104  Mo  192  Wo  368 

Mn  no 
Sideroids,       Sd  Fe     112  Ru   Ir      386 

Ni    116 

Palladoids,     Ud  Co  Pd  Pt     390 

Cuproids,        Kl)  Cu    127  Ag   216  Au    394 


ATOM-MECHANICS.  29! 


In  this  work  we  cannot  undertake  to  enter  further  upon 
this  subject. 

We  hope  to  take  up  this  subject  in  a  separate  treatise  as 
soon  as  time  and  conditions  shall  allow. 

IV.    ATOM-MECHANICS. 

But  that  work  thus  indicated  must  be  preceded  by  our 
Mechanics  of  the  three  States  of  Matter,  giving  the  mechani- 
cal laws  of  the  fusing  and  boiling  points. 

The  contents  of  this  work,  which  has  occupied  my 
thoughts  for  so  many  years  are  foreshadowed  mainly  in  the 
following  publications  of  mine: 

Programme  der  Atomechanik,  1867;  4°,  44  pp. 

Contributions  to  Molecular  Science,  4  Nos.,  8°,  1868, 
32  pp;  1869,  24  pp. 

The  Principles  of  Pure  Crystallography,  1870;  8°,  48  pp. 

Beitrage  zur  Dynamik  des  Chemischen  Molekuls,  1872, 
1873. — Special  Edition,  Leipzig,  1892;  8°,  pp.  24. 

The  Principles  of  Chemistry  and  Molecular  Mechanics, 
1874;  8°,  192  pp. 

SitzungsberichtC)  K.  K.  Akademie  der  Wissenschaften, 
Vienna,  I,  vol.  61  and  II,  vol.  62 ;  1870. 

Comptes  Rendus  of  the  Academy  of  Sciences  of  Paris, 
from  1873  *°  I9OO?  over  thirty  notes,  4°. 

Introduction  to  General  Chemistry,  1897;  8°,  400  pp. — 
Mainly:  Lectures,  91  to  100,  pp.  350  to  382,  and  Plates 
74-80  and  pp.  394-399- 


292  THE   WORK    UNDERTAKEN. 

V.     EPILOGUE. 

In  concluding  this  laborious  work,  extending  over  a  life- 
time, I  beg  permission  to  make  a  personal  statement  which 
it  will  be  well  for  the  reader  to  keep  in  mind  when  meeting 
the  Stasian  dupes — often  in  high  and  influential  stations — 
after  the  publication  of  this,  our  work. 

The  Work  Undertaken. 

Ever  since  I  understood  the  conditions  of  the  chemical 
elements  in  reference  to  a  single,  primitive  substance,  (that 
is,  since  1855),  I  have  most  faithfully  labored  in  this  field, 
mainly  in  the  following  three  directions: 

I.  In  the  Laboratory  by  EXPERIMENTATION  and  in  the 
field  and  sky  by  OBSERVATION,  the   most  thorough  under- 
standing of  the  true  groundwork  of  physical  and  chemical 
science  was  sought. 

In  my  Elements  of  Physics  (1870),  of  Chemistry  (1871), 
and  in  the  method  of  Quantitative  Induction  (1872),  this 
groundwork  was  used  in  the  instruction  of  very  large  classes, 
the  largest  laboratory  classes  in  America  at  that  time. 

II.  The  great  MASTERS  OF  THE  PAST  and  FOUNDERS  OF 
MODERN    SCIENCE   were    most    diligently  studied,   without 
regard  to  difficulties  in  the  way;  they  became,  in  fact,  my 
teachers,   because  I  was   determined   to   learn   from   their 
works  how  they  solved  great  problems  and  how  they  pre- 
sented their  results. 

I  trust  that  I  have  not  been  so  much  with  Newton,  Kepler, 
Galileo  and  Copernicus,  without  learning  something  from 
them  by  the  study  of  their  original  publications. 

But  I  have  also  studied  with  THE  ANCIENT  MASTERS,  not 
only  with  Archimedes  and  Hipparchus,  but  also  with  Plato 
and  Pythagoras. 

With  admiration  and  with  awe  I  have  learned  to  read 
with  understanding  the  most  general  result  of  all  true 
modern  science  in  the  BOOK  OF  WISDOM  dating  back  three 
thousand  years: 

u  Thou  hast  disposed  all  things  wisely  according  to 
(t  measure,  number  and  weight." 


SHAM    EVOLUTION. 


293 


The  evolutionist  of  to-day  is  welcome  to  ridicule  me  for 
this  declaration ;  he  will  thereby  hit  Berzelius  just  as  hard  as 
myself. 

Evolution  is  the  "  Tischlein  decke  dich "  and  the 
"  Eslein  strecke  dich"  of  to-day;  for  its  votaries  believe 
that  everything  just  "  develops  "  without  an  effort  or  a  cause 
or  power;  and  that  this  goes  on  nicely  and  smoothly,  with- 
out a  jar. 

"The  survival  of  the  fittest"  has  become  the  maxim  of 
personal  and  national  morals.  It  is  very  pleasant  to  the 
survivor,  though  he  may  before  God  be  the  greatest  brute  or 
criminal. 

Such  a  doctrine  is  scientifically  absurd  and  morally  per- 
nicious. 

From  day  to  day  the  weather  gets  more  and  more  oppres- 
sive— that  may  be  taken  as  gradual  evolution ;  then  comes 
the  conflict  in  a  storm,  and  purity  is  restored  and  vigor 
returned. 

In  nations,  exactly  the  same.  They  gradually  progress 
apparently — but  actually  get  into  ruts  and  become  rotten. 
A  war,  or  a  revolution,  either  awakes  their  energies  and 
restores  them,  or  subdues  and  destroys  them. 

Just  so  in  science.  The  little  new  done  to-day  is  magni- 
fied a  thousand  fold  by  a  servile  press,  and  by  dependents 
wishing  favors. 

Criticism  of  the  living  authority  is  denounced — but  the 
great  masters  of  the  past  are  robbed  and  insulted  with 
impunity. 

Sham-accuracy  and  show-exhibitions  are  crowned  with 
honors;  while  those  who,  disregarding  human  authority 
would  seek  truth  of  nature  only,  are  stoned  or  starved. 

We  have  incidentally  been  compelled  to  show  such  con- 
ditions in  high  circles  in  some  of  the  capitals  of  Europe; 
and  we  have  seen  that,  even  in  this  direction,  America  leads 
the  world. 

III.  Finally,  I  have  for  almost  half  a  century  diligently 
taken  note  of  IMPORTANT  DETERMINATIONS  in  the  various 
fields  covered  by  the  work  imposed  upon  me. 


394  NEWTON    DENOUNCED. 

In  this  book,  I  have  presented  those  determinations  only 
which  relate  to  the  ATOMIC  WEIGHTS  OF  THE  ELEMENTS. 

While  it  was  not  possible  to  make  the  fourth  part  as  com- 
plete as  intended,  I  feel  confident  that  no  result  of  value  or 
importance  has  been  omitted. 

Truth  Denounced  and  Error  Sustained. 

With  regret,  I  must  admit  that  I  have  been  positively 
"denounced"  for  this  work*  of  mathematically  demonstrat- 
ing a  great  general  scientific  principle  by  the  facts  of 
experiment  and  observation. 

If  our  scientific  editors  and  modern  authors  in  science 
would  learn  just  a  little  before  they  teach,  write  or  denounce — 
they  would  not  disgrace  themselves  before  the  scientific 
public  of  the  Future. 

An  Editor  of  a  Weekly  Journal  of  Chemistry,  published 
in  London,  might  be  expected  to  know  the  name  and  the 
character  of  the  work  of  Newton  sufficiently,  not  to  rush  a 
denunciation  into  his  editorial  column  against  a  chemist, 
whose  work  he  does  not  understand  any  more  than  the 
method  and  work  of  Newton,  which  his  denunciation  hits 
fully  as  much. 

The  supposition  that  in  these  days  of  vaunted  enlighten- 
ment and  general  culture,  a  new  scientific  truth,  fully  dem- 
onstrated by  established  facts,  needs  only  to  be  published  to 
be  accepted,  is  contrary  to  experience,  which  has  proved, 
that  scientific  authorities  of  to-day  are  just  as  rock-rooted 
in  error  and  just  as  prone  to  denounce  and  to  persecute,  as 
the  most  notorious  bigots  and  heretic  burners  of  three  and 
four  centuries  ago. 

It  is  a  most  deplorable  fact  that  our  own  once  mentally 
free  country  has,  at  public  expense  of  many  millions  a  year, 
built  up  the  most  absolute  and  most  harmful  power  working 
for  error  and  enforcing  such  errors  by  official  National  and 
State  authority. 

The  act  of  the  Secretary  of  the  Smithsonian  Institution 
in  officially  declaring  the  false  atomic  weights  of  Clarke  to 

*  Chemical  News,  vol.  73,  p.  232 ;  1896. 


THE    WORK    IS   DONE.  295 

be  true,  is  infinitely  more  harmful  and  condemnable  than 
any  action  against  science  ever  ascribed  to  the  church  or  to 
churchmen. 

For  the  "Smithsonian  Institution  was  founded"  for  the 
increase  and  diffusion  of  KNOWLEDGE  among  men  per 
orbem,"  while  the  church  and  its  officers  have  no  direct 
interest  in  or  obligations  to  scientific  knowledge  and  prog- 
ress. 

But  when  men  who  have  no  understanding  of  science 
have  the  absolute  management  of  great  scientific  institutions 
and  "  bureaus,"  we  cannot  expect  anything  else  than  what  is 
actually  produced,  namely,  the  increase  and  diffusion  of  rot 
and  error  among  men  ee  per  orbem." 

The  Work  is  Done. 

While  young  and  without  experience,  we  suppose  that 
truth  only  needs  to  be  presented  in  order  to  be  accepted. 

But  if  this  truth  be  contrary  to  an  error  established  in 
the  minds  of  men  occupying  prominent  positions,  truth  will 
simply  appear  as  an  enemy  to  these  men  and  will  be 
denounced  and  fought  by  them  with  all  the  power  of  their 
station. 

For  errors  are  like  thorns  and  thistles,  that  grow  easily 
without  labor  or  skill,  while  truth  is  a  tender  plant,  requir- 
ing careful  cultivation  by  hard  labor,  to  subdue  the  weeds 
of  error  that  dispute  the  ground. 

Truly  it  has  been  said:  "  Thorns  also,  and  thistles  shall 
"  it  bring  forth  to  thee  "  and  "  in  the  sweat  of  thy  face  shalt 
"  thou  eat  bread." 

So  it  has  been — so  it  is — and  so  it  will  continue  while 
man  remains. 

Earnestly  have  I  striven  and  faithfully  have  I  labored  in 
this  vineyard  for  almost  half  a  century. 

May  the  spirit  of  truth  and  wisdom  accept  the  work  now 


THE  FIFTEEN  CHEMISTS 

WHOSE  EXPERIMENTAL  DETERMINATIONS  PERMIT  THE 

ESTABLISHMENT  OF  THE  ABSOLUTE  ATOMIC 

WEIGHTS  GIVEN  IN  PART  FOURTH. 


ROSE,  HEINRICH.  Born  August  6,  1795;  died  January  27, 
1864,  at  Berlin,  GERMANY.  Worked  in  the  laboratory  of 
Berzelius.  Professor  of  Chemistry,  University  of  Berlin. 

TITANIUM,  270-271. 

SCHROTTER,  ANTON  RITTER  VON.  Born  November  26, 
1802;  died  April  15,  1875,  at  Vienna,  AUSTRIA.  Professor  of 
Chemistry,  University  of  Vienna. 

PHOSPHORUS,  262-263. 

EBELMEN,  JACQUES-JOSEPH.  Born  at  Beaume-les-Dames, 
July  10,  1814;  died  March  31,  1852,  at  Paris,  FRANCE.  Pro- 
fessor of  Chemistry,  Ecole  des  Mines,  Director  of  the 
Porcelain  Works  at  Sevres. 

URANIUM,  271-272. 

ERDMANN,  AXEL  JOAKIM.  Born  August  12,  1814;  died 
December  i,  1869,  at  Stockholm,  SWEDEN.  Worked  in  the 
laboratory  of  Berzelius;  later  State  Geologist  of  Sweden. 

ZINC,  276-278. 

MARIGNAC,  JEAN  CHARLES,  GALISSARD  DE.  Born  April 
24,  1817;  died  April  15,  1894,  at  Geneva,  SWITZERLAND. 
Student  of  Liebig  and  Dumas.  Professor  of  Chemistry  and 
Mineralogy  at  Geneva  Academy  and  University.  When,  in 
old  age,  unable  to  go  to  the  University,  he  kept  at  work  in 
his  own  laboratory  in  his  own  house. 

BROMINE,  238.     IODINE,  258.     Also :  Pb,  89.     Ag,  90. 

N,  163,  188-189,  192. 

MAUMENE,  EDME  JULES.  Born  November  18,  1818.  Pro- 
fessor of  Chemistry,  Institute  Catholique,  Lyons,  FRANCE. 

SILVER,  221-225.     Also:  Ag,  53.     Fe,  93. 
HAUER,  KARL,  RITTER  VON.     Born  March  3,  1819;  died 
August    2,    1880,    at    Vienna,    AUSTRIA.     Chemist    o^    the 
Reichsanshalt  since  1855. 
CADMIUM,  239-240. 


THE    FIFTEEN.  297 


LOUYET.  Young  Chemist -at  Paris,  FRANCE  ;  died  from 
the  poisonous  effect  of  fluorine,  while  determining  its  atomic 
weight,  1849. 

FLUORINE,  242-243. 

SCHNEIDER,     ERNST    ROBERT.     Born    March    20,    1825. 
Professor  extraordinarius  of  Chemistry,  University  of  Berlin. 
The  last  one,  at  Berlin,  GERMANY,  faithful  to  Berzelian 
traditions;  hence  his  great  success  in  atomic  weight  deter- 
mination. 

ANTIMONY,    265-266.       BISMUTH,    237.       WOLFRAM, 

273-276. 

ROSCOE,  SIR  HENRY  (ENFIELD).  Born  January  7,  1833, 
at  London,  ENGLAND.  Professor  of  Chemistry,  Owen's 
College,  Manchester  (1857-1887);  Vice-Chancellor  of  the 
University  of  London  (1896). 

VANADIUM,  273.    Also :  C,  102,  104.    Wo,  274-275. 
WINKLER,  CLEMENS  ALEXANDER.     Born  December  26, 
1838,  at  Freiburg,  Saxony,  GERMANY.     Professor  of  Chem- 
istry at  the  Bergakademie  at  Freiburg,  since  1873. 
INDIUM,  250. 

NILSON,  LARS  FREDERIK.  Born  May  27,  1840,  at  Skon- 
berga,  Soderkoping,  SWEDEN.  Professor  of  Chemistry, 
Upsala  University. 

BERYLLIUM,  237. 

THORPE,  THOMAS  EDWARD.  Born  December  8,  1845,  at 
Manchester,  ENGLAND.  Professor  of  Chemistry,  Royal 
College  of  Science,  London  (1885);  now  Director  of 
Government  Laboratories,  London. 

SILICON,  267.  Also  :Au,  234.  Br,  238.  Ti,  270-271.  52. 
PETTERSSON,  SVEN  OTTO.     Born  February  12,   1848,  at 
Gothaborg,  SWEDEN.     Professor  of  Chemistry  at  the  Uni- 
versity (Hogskola)  of  Stockholm. 

SELENIUM,  269.     Also :  Be,  237. 

SMITH,  EDGAR  F.  Born  May  23,  1854,  at  York,  in 
Pennsylvania,  UNITED  STATES.  Professor  of  Chemlstrv, 
University  of  Pennsylvania,  at  Philadelphia  (since  1881). 

ARSENIC,  226-231.    Also  :Cd,  239.    Mo,  260.    Pd,  263. 
Sb,  265-6.     Wo,  274-6.     30. 


HONOR  LIST  OF  CHEMISTS. 

Counting  the  two  German-Austrians  to  Germany,  the 
one  Anglo-American  to  the  English,  and  the  one  French- 
Swiss  to  France,  we  find: 

The  12  Founders — 2  Swedes,  5  Eng.,  4  Germans,  i  French. 
"     15  Part  IV.  —3        "        3      "      5         "          4       " 
"    27  Chemists— 5        "8*9         "          5       " 

This  honor  list  of  Chemists  having  distinguished  them- 
selves bj  reliability  and  precision  in  atomic  weight  work, 
permitting  the  establishment  of  absolute  atomic  weights 
by  our  method,  shows  some  very  striking  facts  greatly  at 
variance  with  commonly  received  opinions  concerning  the 
standing  of  the  leading  Nations  in  Chemistry. 

The  Germans  are  supposed  to  lead,  far  ahead  in  the  race. 
The  French  admit  that  (since  1870),  and  now,  even  under 
Moissan,  slavishly  adopt  the  atomic  weights  of  the  a  THREE 
GERMAN  CHEMISTS,"  and  fail  to  recognize  them  to  be  false 
even  after  it  has  been  demonstrated  by  me  in  their  own 
Comptes  Rendus.  See  pp.  153-157.  The  English,  by  the 
Germans  and  the  French,  are  supposed  to  bring  up  the  rear, 
at  a  very  slow  pace;  and  many  of  the  English,  in  public 
print,  growlingly  admit  that  position  and  demand  the 
imitation  of  German  ways.  Finally,  nobody  seems  to 
think  that  there  still  are  excellent  Chemists  in  Sweden; 
some  leading  German  Chemists  actually  publish  old  Berzel- 
ian  ideas  as  "new  discoveries." 

But  the  above  little  table  shows  that,  as  a  matter  of  fact, 
Sweden,  in  numbers,  equals  France;  in  actual  work,  past 
and  present,  it  outranks  France,  as  much  as  Berzelius 
surpassed  Dumas,  whose  great  work  of  his  early  days  is 
forgotten  and  even  condemned  by  the  present  Chemical 
leaders  in  Fracice. 


HONOR   LIST   OF    CHEMISTS.  299 

And  the  English  growlers  at  their  supposed  inferiority, 
are  wonderfully  leading  the  -world  in  solid  Chemical  work. 
It  is  true,  they  have  caught  the  infection  from  Stas,  and 
their  conclusions  are  sometimes  badly  in  error:  but  their 
actual  -work,  done  in  their  despised  little  laboratories,  is  sound 
and  trite,  like  the  old  race  itself;  indeed,  I  confess  that  even 
the  aberrations  of  Crookes  (probably  due  to  his  early  asso- 
ciation with  Hofmann)  are  most  fascinating,  because  they 
are  superficial  only,  not  affecting  the  core,  the  real  deter- 
minations, which  I  have  properly  recognized  as  Berzelian 
(p.  138). 

There  can  be  no  doubt,  to-day  THE  ENGLISH  CHEMISTS 
LEAD  THE  WORLD,  surely  in  this,  the  highest  field  of  Chem- 
istry. The  names  of  Crookes,  Ramsay  and  Rayleigh  are 
stars  of  first  magnitude,  and  will,  we  hope,  continue  to 
radiate  solid  and  profound  truth  for  many  years  to  come. 

The  other  English  Chemists,  Roscoe  and  Thorpe,  are 
fully  equal  to  any  worker  to-day  in  Germany.  In  France, 
under  the  scepter  of  Moissan,  we  find  no  serious  work  done 
in  this  field;  only  false  work  is  awarded  academic  honors 
PP-  16,  (34,  151-158,  170- 

GERMANY,  in  numbers,  barely  exceeds  England ;  but  its 
great  laborers  in  this  field  are  all  resting  from  the  noble 
work  they  have  done— and  their  glory  is  dragged  in  the 
Stasian  mire  by  the  living  Coal  Tar  Chemists. 

Only  Clemens  Winkler  and  Karl  Seubert,  are  working 
to-day  in  the  way  of  the  old  master  Berzelius;  these  two 
alone,  in  the  magnificently  endowed  laboratories  of  the 
great  Universities  of  Germany.  Even  the  interesting  text 
book  of  Erdmann  does  not  know  the  work  of  Swedish  and 
German  Chemists  of  that  great  name,  but  gives  the  entire 
modern  corruption  of  Stas,  Lothar  and  Dmitry. 

From  America,  we  have  been  able  to  admit  only  one  name 
to  this  honor  list,  although  so  many  are  doing  "  atomic 
weight  work"  as  they  have  learned  it  in  Germany,  where 
already  old  Chancellor  Koch,  of  Goettingen,  declared : 
Sumimus  pecuniam  et  mittimus  asinum  in  patriam.  (Carl 
Vogt,  aus  meinem  Leben,  1896,  p.  138).  The  influence  of 
this  element  has  been  very  unfavorable. 


300  HONOR   LIST    OF    CHEMISTS. 

This  country  is  too  big  to  remain  a  dependency  of  Ger- 
man Chemistry,  especially  when  that  Chemistry  is  such  as 
it  is  to-day. 

The  worst  permanent  damage  is  done  by  the  encourage- 
ment of  German  ways  in  University  Organization  and 
Scientific  Work  of  the  Nation  and  the  States.  To  copy  the 
German  Army  System  would  not  prove  as  bad  as  what  has 
been  and  is  now  being  done  to  the  scientific  life  of  America. 

What  is  needed,  is  a  manly  independence  of  thought,  not 
a  servile  imitation  of  an  Imperial  Pattern. 

The  Imitation  of  the  Royal  Institution  (only  Royal  in 
name,  being  founded  and  maintained  by  sturdy  burghers  of 
London)  would  be  more  wholesome  than  the  copying  of  the 
formalisms  of  the  Universities  of  the  German  Empire,  with 
its  t{  theses"  and  learning  in  airy  heights  without  visible 
means  of  support  in  nature  or  in  mathematics. 

Finally,  if  we  compare  the  teutonic  nations  to  the 
romanic,  we  have  twenty-two  of  the  first  to  five  of  the  latter 
in  our  honor  list.  For  the  twelve  fundamental  workers,  the 
proportion  is  eleven  to  one. 

May  this  book  definitely  remove  the  noxious  weeds  that 
have  grown  around  the  chemical  monument  erected  by 
Berzelius,  and  may  the  best  and  truest  chemist — also  of  old 
Germany — again  join  in  solid  work,  worthy  of  the  great 
master:  then  we  shall  soon  learn  the  true  value  of  the 
absolute  atomic  weight  of  those  elements  for  which,  at 
present,  we  lack  the  necessary  experimental  data. 


INDEX  OF  NAMES. 


Abrahall,  see  Hoskyns. 

Allen.    Cs,  241. 

Alloy,  J.    False  Data,  35.   Ur, 

272. 

Alphons,  of  Castile,  284. 
Anderson.    Pb,  87. 
Arbuckle.    Cd,  239. 
Archimedes,  of  Syracuse,  Ar- 

enary,  286,  292. 
ASTON.     See  p.  ix. 


Bailey.     Pd,  263.     Zr,  278. 
Barker.    Weighing,  275. 
Baubigny.    Al,  225. 
Bauer.    La,  259. 
Baxter.    Fe,  94-95. 
Becker.    Recalcul.,  75,  79,  So. 
Benoist.    In,  258. 
Berlin.    Cr,  241. 
Bernoulli.     Wo,  274-5. 
BERZELIUS.     See  p.  vm. 
Boehringer.     Assignor,    206. 
Bongartz.    Sb,  266.  Sn,  267-8. 
v.  Borch.    Wo,  274-5. 
Brahe,  see  Tycho. 
Brauner.     Ce,  240.     La,  259. 

Te,  269-70. 
Breed.    Pd,  263. 
Bucher.    Cd,  239-40. 
Buehrig.     Ce,  240. 
Bunsen.    Cs,   241.      In,   2t;8. 

Rb,  264.     ' 


Burton.     Zn,  276. 

Chauvenet.    Astronomy,  197. 
Chee,  210. 

Clarke,    15-18,  23,  28,  46,  72, 
75,  78-9,  9i,  99,  101,  105, 

109,     112-13,     122,    140,    150, 

160-6,    171,   184,    195,    199, 

203, 208,  221-3, 228-9, 234-5, 

271-2,  etc. 
Classen.     Sn,  367-8. 
Cleve.     La,  259. 
Commaille.     Cu,  242. 
Cooke.     Br,   238.     S,    264-5. 

Sb,  265-6. 
Copernicus.     292. 
Cornu.    Syst.  Errors,  46. 
CROOKES.     See  p.  ix. 

Debray.     Mo,  260. 
De  Luca.     Fl,  243. 
Demoly.    Ti,  270. 
Dewar.     Mn,  260. 
Dexter.     Sb,  266. 
Diehl.     Li,  259. 
Ditmar.     II,  244. 
DUMAS.    See  p.  yin. 

EBELMEX.     See  p.  296. 
Ekman.     Se,  267. 
ERDMANX,  AXEL.    See  p.  296. 
ERDMAXX,  OTTO,    See  p.  vm. 


THE  MECHANISM  OF  THE  AURORA 

lies  in  the  nullovalent  elements  of  the  atmosphere  (p.  220). 
The  common  gases  constitute  FOUR  DISTINCT  STRATA  in 
our  atmosphere,  of  which  the  estimated  thickness  is  here 
given  in  myriameters  (about  six  English  miles  each).  See 
my  papers,  Comptes  Rendus,  August  20,  1900,  and  National 
Druggist,  Sept.  1900. 

I.     LOWER  ATMOSPHERE,  with  aqueous  vapor  and  car- 
bon dioxide,  2  myr. 

II.     OXYGEN  STRATUM,       3  myr.;  from  16  to    10  %  O. 

III.  NITROGEN  STRATUM,    5  myr.;  from  84  to      4  %  N. 

IV.  HYDROGEN  STRATUM,  7  myr.;  from  80  to  100  %  H. 
The    NULLOVALENT    GASES    occur    according    to    their 

densities: 

XENON  and  KRYPTON  in  the  lowest  stratum,  I,  exclusively. 

ARGON  terminates  in  the  oxygen  stratum,  II. 

NEON  is  most  abundant  in  the  upper  half  of  the  nitrogen 
stratum,  III;  while 

HELIUM  prevails  in  the  lower  part  of  the  hydrogen 
stratum,  IV,  reaching  about  16  %. 

The  main  physical  characters  of  these  gases  are:  their 
apparently  high  conducting  power  for  heat  and  electricity, 
together  with  the  brilliant  light  they  emit  under  high  electric 
tension ;  this  light  is  marked  by  characteristic  spectra. 

The  lower  gases,  Xenon  and  Krypton,  thus  must  show 
cloud-formations;  the  brightest  green  crypton  line  of  558 
millimicrons  is  accordingly  most  characteristic  of  the  lower 
aurorae. 

All  these  gases  will,  by  their  greater  electric  conductivity, 
form  mobile  threads  dirigeable  by  the  magnetic  force  of  the 
earth — as  do  the  iron  filings  on  our  glass  plate  above  a 
common  magnet. 

From  Krypton  to  Helium,  thus  beams  may  form  several 
myriameters  in  length,  constituting  great  linear  conductors 
from  the  lower  strata  to  the  highest  hydrogen  stratum. 

These  beams  will  show  colored  light,  varying  according 
to  the  many  varied  conditions  of  pressure,  per. cent  amount, 
intensity  of  discharge  and  kind  of  gas. 

This  I  consider  an  outline  of  the  mechanism  of  the 
Northern  Lights. 

A  paper  on  this  subject  was  apparently  lost  in  the  mails 
a  year  ago;  hence  this  short  note. 


